Three-dimensional molecule generation by noise reduction of voxel grids

Abstract

The voxelized representation of an input molecule can be updated by applying a molecular design computation model trained to approximate a data distribution of molecules exhibiting one or more desired properties. The molecular design computation model can update the voxelized representation of the input molecule to increase the likelihood that the resulting updated voxelized representation is in the data distribution. The voxelized representation of an output molecule can be generated based on the updated voxelized representation. For example, if the molecular design computation model is trained to approximate a noisy data distribution occupied by noisy voxelized representations of molecules exhibiting one or more desired properties, the voxelized representation of the output molecule can be generated by denoising the updated voxelized representation to map the updated voxelized representation from the noisy data distribution to the true data distribution.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims priority to U.S. Provisional Application No. 63 / 502,529, titled "Three - Dimensional Molecule Generation by Voxel Grid Noise Removal", filed on May 16, 2023; U.S. Provisional Application No. 63 / 586,263, titled "Three - Dimensional Molecule Generation by Voxel Grid Noise Removal", filed on September 28, 2023; and U.S. Provisional Application No. 63 / 623,062, titled "Three - Dimensional Molecule Generation by Voxel Grid Noise Removal", filed on January 19, 2024, and the disclosures of these U.S. provisional applications are hereby incorporated by reference in their entirety.

[0002] The subject matter described herein generally relates to generative artificial intelligence, and more specifically to machine - learnable techniques for generating representations of three - dimensional molecules in a discrete and latent voxelized space.

Background Art

[0003] Introduction A molecule is a group of two or more atoms held together by chemical bonds. Molecules form the smallest distinguishable units that can divide a pure substance while still retaining the composition and chemical properties of that substance. An example of a molecule is a small molecule, which is a low - weight compound having a molecular weight of approximately 100 daltons to 1000 daltons. Small - molecule therapeutic agents that regulate biochemical processes for diagnosing, treating, and preventing various diseases are the basis of modern pharmacology due to several compelling advantages. For example, small - molecule drugs can penetrate cell membranes and reach intracellular targets. Further, small - molecule drugs are adaptable to a wide variety of therapeutic uses. For example, small - molecule drugs can be formulated as tablets and capsules, intravenous or subcutaneous injections, inhalants, or suppositories. The development of small - molecule drugs can further extend to adjusting various pharmacokinetic properties, including liberation, absorption, distribution, metabolism, efficacy, effectiveness, action on phenotypes, and excretion.

[0004] In contrast, large molecules (also known as biopharmaceuticals, biologics, or biological drugs) can have molecular weights ranging from approximately 3,000 to 150,000 daltons. Large molecule drugs are often derivatives of native human proteins that modulate many essential cellular functions, such as enzymatic reactions, molecular transport, regulation and execution of several biological pathways, cell proliferation, growth, nutrient uptake, morphology, motility, and intercellular communication. It is common for a single large molecule to have more than 1,300 amino acid residues linked by peptide bonds to form one or more polypeptides. Due to their size and complexity, large molecule drugs are recombinantly produced by engineered cells, rather than being chemically synthesized like most small molecule drugs. Furthermore, large molecule therapeutics are usually delivered by injection or infusion due to their ineffectiveness in oral administration. The development of large molecule drugs may involve designing sequences of one or more amino acid residues that can bind to a target (e.g., protein, nucleic acid, etc.) with sufficient specificity while lacking undesirable characteristics such as immunogenicity, self-association, and instability. [Overview of the Initiative]

[0005] Systems, methods, and products, including computer program products, are provided for generating three-dimensional molecules in voxelized space. In one embodiment, a machine learning-enabled system for generating three-dimensional molecules is provided. The system may include at least one processor and at least one memory. The at least one memory may contain program code that, when executed by at least one processor, brings about an operation. The operation may include identifying an input molecule, generating a voxelized representation of the input molecule, and applying a molecular design computation model to update the voxelized representation of the input molecule, wherein the molecular design computation model is trained to approximate a data distribution of molecules exhibiting one or more desired properties by taking corrupted voxelized representations of sample molecules exhibiting one or more desired properties as input and recovering the voxelized representations of sample molecules from the corrupted voxelized representations of sample molecules, and the molecular design computation model updates the voxelized representation of the input molecule to increase the likelihood that the resulting updated voxelized representation is in the data distribution, and generates a voxelized representation of an output molecule based on at least the updated voxelized representation.

[0006] In another embodiment, a method for machine learning-enabled three-dimensional molecule generation is provided. The method may include: identifying an input molecule; generating a voxelated representation of the input molecule; and applying a molecular design computation model to update the voxelated representation of the input molecule, wherein the molecular design computation model is trained to approximate a data distribution of molecules exhibiting one or more desired properties by taking corrupted voxelated representations of sample molecules exhibiting one or more desired properties as input and recovering the voxelated representations of sample molecules from the corrupted voxelated representations of sample molecules; and applying the molecular design computation model to update the voxelated representation of the input molecule to increase the likelihood that the resulting updated voxelated representation falls within the data distribution; and generating a voxelated representation of an output molecule based on at least the updated voxelated representation.

[0007] In another embodiment, a computer program product for machine learning-enabled three-dimensional molecule generation is provided. The computer program product may include a non-temporary computer-readable medium that stores instructions that cause an action when executed by at least one data processor. The action may include identifying an input molecule, generating a voxelized representation of the input molecule, and applying a molecular design calculation model to update the voxelized representation of the input molecule, wherein the molecular design calculation model is trained to approximate a data distribution of molecules exhibiting one or more desired properties by taking corrupted voxelized representations of sample molecules exhibiting one or more desired properties as input and recovering the voxelized representations of sample molecules from the corrupted voxelized representations of sample molecules, and the molecular design calculation model updates the voxelized representation of the input molecule to increase the likelihood that the resulting updated voxelized representation is within the data distribution, and generating a voxelized representation of an output molecule based on at least the updated voxelized representation.

[0008] In some modifications, one or more features disclosed herein, including the following features, may be arbitrarily included in any feasible combination:

[0009] In some variations, the voxelized representation of a molecule may include multiple voxels organized into a three-dimensional voxel grid. Each atom within the molecule may be represented as a continuous density across one or more voxels in the three-dimensional voxel grid.

[0010] In some variations, the continuity density of each atom within a molecule can be concentrated at the center of each atom. A first voxel located far from any atom within the molecule may be associated with a lower atomic density value than a second voxel located closer to the center of an atom within the molecule.

[0011] In some variations, each voxel in a three-dimensional voxel grid can be associated with a value that indicates the atomic density at its corresponding location.

[0012] In some variations, the voxelized representation of a molecule may contain one or more channels. Each channel may correspond to a type of atom present in the molecule.

[0013] In some variations, applying a molecular design computation model to update the voxelized representation of an input molecule may involve updating the voxelized representation of the input molecule based at least on a function that outputs a value indicating the likelihood that the resulting updated voxelized representation falls within the data distribution.

[0014] In some variations, the function can be parameterized by multiple parameters of the molecular design calculation model.

[0015] In some variations, the function may be a scoring function. The value output by the function may be a score indicating a local change in the density of the data distribution at the location of the updated voxelized representation.

[0016] In some variations, the molecular design computation model may update the voxelized representation of the input molecule by at least updating the voxelized representation of the input molecule to generate a first updated voxelized representation; updating the voxelized representation of the input molecule to generate a second updated voxelized representation; applying a function parameterized by the molecular design computation model to determine a first value indicating a first local change in the density of the data distribution at a first location occupied by the first updated voxelized representation; applying a function to determine a second value indicating a second local change in the density of the data distribution at a second location occupied by the second updated voxelized representation; and further updating the first updated voxelized representation instead of the second updated voxelized representation if the first and second values ​​indicate that the density of the data distribution is higher at the first location than at the second location.

[0017] In some variations, the molecular design calculation model may be applied to further update the first updated voxelized representation until one or more criteria are met.

[0018] In some variations, one or more criteria may include at least one of the following: (i) iterations of the threshold amount update for the voxelized representation of the input molecule have been performed; (ii) the first value of the first updated voxelized representation satisfies one or more thresholds; and (iii) an output molecule of the threshold amount has been generated.

[0019] In some variations, the molecular design calculation model may be applied to further modify the first updated voxelized representation instead of the second updated voxelized representation, at least on the basis that the first and second values ​​indicate that the first updated voxelized representation is more likely to be within the data distribution than the second updated voxelized representation.

[0020] In some variations, the molecular design calculation model may be applied to further modify the first updated voxelized representation in place of the second updated voxelized representation, at least on the basis that the first and second values ​​indicate that the first updated voxelized representation is sampled from a higher data distribution density region than the second updated voxelized representation.

[0021] In some variations, the data distribution may be a noisy data distribution occupied by noisy voxelized representations of molecules exhibiting one or more desired properties. The voxelized representation of the output molecules may be generated by denoising the first updated voxelized representation in order to map the first updated voxelized representation from the noisy data distribution to the true data distribution of molecules exhibiting one or more desired properties.

[0022] In some variations, the voxelized representation of the output molecule can be transformed into a different representation of the output molecule.

[0023] In some variations, different representations of the output molecule may include a one-dimensional representation and / or a two-dimensional representation of the output molecule.

[0024] In some variations, the voxelized representation of the output molecule is transformed by at least detecting one or more peaks of a plurality of atomic density values included in the voxelized representation of the output molecule and determining one or more interconnecting bonds based on at least the positions of one or more atoms, thereby at least determining the positions of one or more atoms within the output molecule.

[0025] A system, method, and product including a computer program product are provided for generating three-dimensional molecules within a voxelized space. In one aspect, a system for machine-learnable three-dimensional molecule generation is provided. The system can include at least one processor and at least one memory. The at least one memory can include program code that, when executed by the at least one processor, causes operations. The operations can include identifying a sample molecule that exhibits one or more desired characteristics, generating a noisy voxelized representation of the sample molecule, adding noise to the noisy voxelized representation of the sample molecule to generate a corrupted voxelized representation of the sample molecule, and training a molecular design computational model to approximate a data distribution of molecules that exhibit one or more desired characteristics, the training including applying the molecular design computational model to recover the noisy voxelized representation of the sample molecule from the corrupted voxelized representation of the sample molecule, and optionally generating a voxelized representation of an output molecule by at least applying the molecular design computational model to denoise a voxelized representation of an input molecule.

[0026] In another embodiment, a method for machine learning-enabled three-dimensional molecule generation is provided. The method includes identifying a sample molecule exhibiting one or more desired properties; generating a noisy voxelated representation of the sample molecule; generating a corrupted voxelated representation of the sample molecule by adding noise to the noisy voxelated representation of the sample molecule; and training a molecular design computation model to approximate the data distribution of a molecule exhibiting one or more desired properties, wherein training includes applying the molecular design computation model to recover the noisy voxelated representation of the sample molecule from the corrupted voxelated representation of the sample molecule; and optionally, generating a voxelated representation of an output molecule by applying the molecular design computation model to at least generate a voxelated representation of an output molecule by at least applying the molecular design computation model to denoise the voxelated representation of an input molecule.

[0027] In another embodiment, a computer program product for machine learning-enabled three-dimensional molecule generation is provided. The computer program product may include a non-temporary computer-readable medium that stores instructions that cause an action when executed by at least one data processor. The action may include identifying a sample molecule exhibiting one or more desired properties; generating a noisy voxelated representation of the sample molecule; adding noise to the noisy voxelated representation of the sample molecule to generate a corrupted voxelated representation of the sample molecule; and training a molecular design computation model to approximate a data distribution of molecules exhibiting one or more desired properties, wherein training includes applying the molecular design computation model to recover the noisy voxelated representation of the sample molecule from the corrupted voxelated representation of the sample molecule; and optionally, generating a voxelated representation of an output molecule by at least applying the molecular design computation model to denoise the voxelated representation of an input molecule.

[0028] In some modifications, one or more features disclosed herein, including the following features, may be arbitrarily included in any feasible combination:

[0029] In some variations, the voxelized representation of the sample molecule with a lot of noise may include a plurality of voxels organized in a three-dimensional voxel grid. Each atom within the sample molecule may be represented as a continuous density spanning one or more voxels within the three-dimensional voxel grid.

[0030] In some variations, the continuous density of each atom within the sample molecule may be concentrated at the center of each atom.

[0031] In some variations, each voxel within the three-dimensional voxel grid may be associated with a value indicating the atomic density at the corresponding location.

[0032] In some variations, a first voxel located away from any atom within the sample molecule may be associated with a lower atomic density value than a second voxel located closer to the center of the atoms within the sample molecule.

[0033] In some variations, the voxelized representation of the sample molecule with a lot of noise may include one or more channels. Each channel may correspond to the type of atom present within the sample molecule.

[0034] In some variations, the voxelized representation of the sample molecule with a lot of noise may represent both the type and position of one or more atoms present within the sample molecule.

[0035] In some variations, the training of the molecular design calculation model may include adjusting a plurality of parameters of the molecular design calculation model to reduce the difference between the recovered voxelized representation of the sample molecule generated by the molecular design calculation model and the voxelized representation of the sample molecule with a lot of noise.

[0036] In some variations, multiple parameters of the molecular design calculation model can parameterize the function. The values ​​of these multiple parameters can be adjusted so that the function outputs values ​​that represent local changes in the density of the data distribution of molecules exhibiting one or more desired properties.

[0037] In some variations, the molecular design computation model can denoise the voxelated representation of the input molecule by updating at least the atomic density of one or more voxels in at least one channel of the voxelized representation of the input molecule.

[0038] In some variations, updating the atomic density of one or more voxels within at least one channel of the voxelized representation of the input molecule may correspond to updating at least one of the types and / or positions of one or more atoms present in the input molecule.

[0039] In some variations, molecular design computation models can denoise the voxelized representation of an input molecule across multiple iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling until one or more criteria are met.

[0040] In some variations, one or more criteria may include at least one of the following: (i) an iteration of a threshold quantity of gradient-based Markov chain Monte Carlo (MCMC) sampling has been performed; (ii) a voxelized representation of the output molecule has been sampled from a region having a threshold density; and (iii) an output molecule of a threshold quantity has been generated.

[0041] In some variations, the molecular design computation model generates a voxelized representation of an output molecule by, at least, applying a first update to the voxelized representation of the input molecule to generate a first updated voxelized representation, applying a second update to the voxelized representation of the input molecule to generate a second updated voxelized representation, and further updating the first updated voxelized representation when it is determined that the first updated voxelized representation is sampled from a higher data distribution density region than the second updated voxelized representation.

[0042] In some variations, the data distribution may be a noisy data distribution occupied by noisy voxelized representations of molecules exhibiting one or more desired properties. The voxelized representations of the output molecules may be further generated by denoising the first updated voxelized representations to map them from the noisy data distribution to the true data distribution of molecules exhibiting one or more desired properties.

[0043] In some variations, the voxelized representation of the output molecule can be transformed into a different representation of the output molecule.

[0044] In some variations, different representations of the output molecule may include a one-dimensional representation and / or a two-dimensional representation of the output molecule.

[0045] In some variations, training a molecular design computation model may include applying a molecular design computation model having a first adjustment to denoise a corrupted voxelated representation of a sample molecule to generate a first recovered voxelated representation of the sample molecule; determining a first mean squared error (MSE) that quantifies a first difference between the first recovered voxelated representation and a noisy voxelated representation of the sample molecule; applying a molecular design computation model having a second adjustment to denoise a corrupted voxelated representation of the sample molecule to generate a second recovered voxelated representation of the sample molecule; determining a second mean squared error (MSE) that quantifies a second difference between the second recovered voxelated representation and a noisy voxelated representation of the sample molecule; and further adjusting the molecular design computation model having the first adjustment instead of the second adjustment when determining that the first mean squared error (MSE) is smaller than the second mean squared error (MSE).

[0046] Implementations of this subject matter may include, but are not limited to, methods provided herein, and articles comprising a tangibly embodied machine-readable medium capable of causing one or more machines (e.g., a computer) to perform one or more of the features described herein. Similarly, computer systems may include one or more processors and one or more memories coupled to one or more processors. A memory, which may include a non-temporary computer-readable or machine-readable storage medium, may contain, encode, or store one or more programs causing one or more processors to perform one or more of the operations described herein. Computer implementations consistent with one or more implementations of this subject matter may be implemented by one or more data processors present in a single computing system or in multiple computing systems. Such multiple computing systems may be connected and may exchange data and / or commands or other instructions, etc., via one or more connections, including, for example, connections across networks (e.g., the Internet, a wireless wide area network, a local area network, a wide area network, a wired network, etc.), connections via direct connections between one or more of the multiple computing systems.

[0047] Details of one or more variations of the subject matter described herein are described in the accompanying drawings and the following description. Other features and advantages of the subject matter described herein will become apparent from the description and drawings, as well as from the claims. Certain features of the subject matter currently disclosed are described for illustrative purposes in relation to the computational design of molecules, including drug molecules, but it should be readily apparent that such features are not intended to be limiting. The claims following this disclosure define the scope of the subject matter to be protected. [Brief explanation of the drawing]

[0048] The accompanying drawings incorporated herein and constituting part of this specification illustrate specific aspects of the subject matter disclosed herein and, together with the description, help to illustrate some of the principles relating to the disclosed implementations. In the drawings,

[0049] [Figure 1A] A diagram of a system illustrating an example of a molecular design system according to several exemplary embodiments is drawn.

[0050] [Figure 1B] A system diagram is drawn showing another example of a molecular design system according to several exemplary embodiments.

[0051] [Figure 2] A flowchart illustrating an example of a process for machine learning-enabled generation of three-dimensional molecules in a voxelized space, according to several exemplary embodiments, is drawn.

[0052] [Figure 3A] A flowchart illustrating an example of the process for training a molecular design computation model to generate three-dimensional molecules in a voxelized space, according to several exemplary embodiments, is drawn.

[0053] [Figure 3B] A flowchart is drawn illustrating another example of the process for applying a molecular design computation model to generate a three-dimensional molecule in a voxelized space, according to several exemplary embodiments.

[0054] [Figure 3C] A flowchart illustrating an example of the process for applying a molecular design computation model to generate a three-dimensional molecule in a voxelized space, according to several exemplary embodiments, is drawn.

[0055] [Figure 4] An example of a voxelized representation of a molecule, according to several exemplary embodiments, is depicted.

[0056] [Figure 5A] A schematic diagram is drawn illustrating an example of the process for training a denoising engine to denoise noisy voxelized representations of molecules, according to several exemplary embodiments.

[0057] [Figure 5B] A schematic diagram illustrating an example of a walk-jump sampling method according to several exemplary embodiments is shown.

[0058] [Figure 5C] A schematic diagram illustrates an example of the process in a molecular design computation model for generating three-dimensional molecules by denoising voxelized molecular representations, according to several exemplary embodiments.

[0059] [Figure 5D] A schematic diagram is drawn illustrating an example of a process for generating other molecular representations from voxelized representations of molecules, according to several exemplary embodiments.

[0060] [Figure 6] A schematic diagram illustrates an example of the process of a molecular design computation model for generating a voxelized representation of a molecule by operating in a noisy, potential voxelized space, according to several exemplary embodiments.

[0061] [Figure 7] A graph is drawn showing the effect of noise levels on the generation performance of molecular design calculation models according to several exemplary embodiments.

[0062] [Figure 8] A schematic diagram illustrating the effect of the number of sampling iterations in Markov chain Monte Carlo (MCMC) sampling on the generation performance of molecular design calculation models according to several exemplary embodiments is shown.

[0063] [Figure 9A]This section illustrates examples of voxelized representations of molecules generated by molecular design computation models trained on the QM9 molecular dataset, according to several exemplary embodiments.

[0064] [Figure 9B] This section illustrates examples of voxelized representations of molecules generated by molecular design computation models trained on molecular geometric ensemble (GEOM) drug datasets, according to several exemplary embodiments.

[0065] [Figure 10A] The graphs show the cumulative distribution function (CDF) of strain energy for molecules in the QM9 molecular dataset, molecules generated by conventional generative models, and molecules generated by molecular design computation models trained on the QM9 molecular dataset, according to several exemplary embodiments.

[0066] [Figure 10B] A graph is drawn showing the empirical distribution of the number of atoms per molecule in the QM9 molecular dataset, compared to the empirical distribution of the number of atoms in molecules generated by molecular design computation models trained on the QM9 molecular dataset, according to several exemplary embodiments.

[0067] [Figure 11A] The graphs illustrate the cumulative distribution function (CDF) of strain energy for molecules in a geometric ensemble (GEOM) drug dataset, molecules generated by conventional generative models, and molecules generated by molecular design computation models trained on the GEOM drug dataset, according to several exemplary embodiments.

[0068] [Figure 11B] A graph is drawn showing the empirical distribution of the number of atoms per molecule in a geometric ensemble of molecules (GEOM) drug dataset, compared to the empirical distribution of the number of atoms in molecules generated by a molecular design computation model trained on the GEOM drug dataset, according to several exemplary embodiments.

[0069] [Figure 12A] A schematic diagram is drawn to show a comparison of the seed-generating performance of geometric ensemble (GEOM) drugs for molecules in discrete and latent voxelization spaces, according to several exemplary embodiments.

[0070] [Figure 12B] A schematic diagram is drawn to show a comparison of seed generation performance for PubChem drugs in discrete voxelization spaces and potential voxelization spaces, according to several exemplary embodiments.

[0071] [Figure 12C] Plot molecular graphs of additional examples of molecules generated by performing seed generation in the potential voxelization space for actual drugs.

[0072] [Figure 12D] Plot molecular graphs of additional examples of molecules generated by performing de novo synthesis in a potential voxelization space on actual drugs.

[0073] [Figure 13] The graphs illustrate a comparison of seed generation performance for geometric ensemble (GEOM) drugs of molecules in discrete and latent voxelization spaces, according to several exemplary embodiments.

[0074] [Figure 14] A block diagram is drawn showing an example of a computing system according to several exemplary embodiments.

[0075] In practical terms, similar reference numbers indicate similar structures, features, or elements. [Modes for carrying out the invention]

[0076] Detailed explanation Generating new molecules with desired properties is a crucial task in chemistry, with applications across many scientific fields. In the context of drug discovery, conventional computational techniques for generating molecules with drug-like properties require exploring the molecular space (or chemical space) occupied by all possible chemical compounds (e.g., every possible combination of atoms of two or more chemical elements). For example, some search-based approaches may involve scoring and ranking different molecules within the molecular space based on one or more drug-like properties such as affinity, specificity, biological activity, and suitability for development. However, 10 60 The aforementioned molecular space, estimated to contain 100 million conceivable chemical compounds, is enormously large and scales exponentially with molecular size (e.g., the number of constituent atoms). Even a tiny fraction of this molecular space can contain billions to trillions of molecules. With state-of-the-art computing resources, conventional search-based methods can only explore small portions of the molecular space, such as small regions of the molecular space selected based on prior domain knowledge. This limitation in search scope means that conventional search-based approaches are likely to overlook molecules with more optimal properties. Furthermore, because conventional search-based methods do not explore the molecular space in a principled way, they prevent the generation process from being conditioned on specific properties.

[0077] Furthermore, whether a molecule exhibits specific desired properties can depend on its conformation (or three-dimensional structure). For example, the binding affinity between a drug molecule and a target molecule (e.g., a protein, nucleic acid, etc.) may depend on the drug molecule's ability to adopt a conformation (or three-dimensional structure) complementary to the target molecule's conformation. Moreover, molecules are flexible, meaning that a single molecule can adopt one of many possible conformations (or three-dimensional structures). In some cases, a group of the same molecules can exist as a collection of many different conformations in equilibrium with each other, but not all possible conformations are associated with the desired properties. In relation to binding affinity, for example, the biologically active conformation of a molecule may be one or more of the conformations exhibited by the molecule in solution, or new conformations induced by interaction with the target molecule. However, one-dimensional representations of molecules (e.g., Simplified Molecular Input Line Input System (SMILES) strings) or two-dimensional representations (e.g., molecular graphs) do not adequately capture the conformation (or three-dimensional structure) of a molecule. Therefore, if a molecular design calculation model operates on a one-dimensional or two-dimensional representation of the input molecule, the resulting output molecule may not exhibit one or more desired conformations (or three-dimensional structures) associated with those properties.

[0078] Various exemplary embodiments of this disclosure can improve current state-of-the-art computing resources by providing molecular design computation models that can generate output molecules by exploring molecular space (or chemical space) in principle, rather than indiscriminately searching a limited portion of molecular space. For example, in some cases, the molecular design computation model may be trained to approximate a data distribution of molecules exhibiting one or more desired properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development). Training the molecular design computation model may include determining the parameters of a function (e.g., a score function) such that the output of the function is a value that indicates the change in density across the data distribution. In some cases, the molecular design computation model may sample the data distribution to generate output molecules that also exhibit one or more desired properties. For example, in some cases, the molecular design computation model may sample the data distribution by denoising input molecules, such as voxelized representations of the input molecules, over a plurality of sampling iterations. During each sampling iteration, the molecular design computation model may update the input molecules to remove some of the noise present in the input molecules. In doing so, it may generate updated molecules (e.g., voxelized representations of the updated molecules) that constitute a selected sample from the data distribution. As described in more detail below, sampling can be guided by a function such that each successive sample (or updated molecule) is selected from an increasingly dense region of the data distribution, where it is more likely to be occupied by molecules exhibiting one or more properties.

[0079] In some exemplary embodiments, the likelihood that the output molecule will exhibit one or more desired properties can be increased (or maximized) by a molecular design computation model operating on a three-dimensional representation of the input molecule. For example, in some cases, the molecular design computation model may generate the output molecule by at least denoising the three-dimensional representation of the input molecule, for example, over multiple sampling iterations. In some cases, the molecular design computation model may generate the output molecule by denoising a voxelized representation of the input molecule instead of a conventional three-dimensional representation of the input molecule. Conventional three-dimensional representations of an input molecule, such as a point cloud representation of the input molecule, can specify the conformation (or three-dimensional structure) of the input molecule by at least specifying the coordinates of the constituent atoms (e.g., in Euclidean space). However, conventional three-dimensional representations of input molecules may impose some limitations on the generation process. For example, for a molecular design computation model to operate on a conventional three-dimensional representation of the input molecule, the number of atoms in the output molecule generated from it must be known in advance. Denoising conventional three-dimensional representations of input molecules may also require specific workarounds to allow molecular design computation models to approximate the distribution of atom types within the output molecule, which may form a discrete distribution, while the positions of atoms within the output molecule (e.g., atomic coordinates in Euclidean space) may form a continuous distribution. Furthermore, conventional three-dimensional representations of input molecules may not adequately capture long-range dependencies that exist across multiple atoms, especially as the number of constituent atoms increases.

[0080] In some exemplary embodiments, a voxelized representation of a molecule (e.g., an input molecule) can overcome the aforementioned limitations by representing the input molecule as a continuous distribution of atomic density across a voxel grid, centered on the atomic coordinates of the individual atoms present in the molecule. For example, in a graph network representation of a molecule, the dependency between two adjacent atoms may be represented by interconnection edges. However, these edges may not adequately capture longer-range dependencies, such as dependencies between non-adjacent atoms. In contrast, even when the input molecule contains a large number of atoms, a voxelized representation of a molecule can better capture long-range dependencies between distant atoms. Furthermore, a molecular design computation model can operate on a voxelized representation of an input molecule to generate an output molecule without prior knowledge of the number of atoms present in the output molecule. This is because the molecular design computation model can freely add or remove different types of atoms by updating the distribution of atomic density across the voxel grid. The voxelized representation of the input molecule also represents both the type and position of atoms within the input molecule, thereby eliminating the need for workarounds to match two different types of data distributions (e.g., a discrete distribution of atom types and a continuous distribution of atom positions).

[0081] In some exemplary embodiments, a voxelized molecular representation of a molecule, such as an input molecule, may represent each atom in the molecule (e.g., the input molecule) as a continuous (e.g., Gaussian) density across one or more voxels in a voxel grid. In this context, the voxel grid is a three-dimensional grid of voxels organized into continuous layers of rows and columns. Various examples of voxel grids described herein may include multiple voxels, each of which is a volume element (e.g., a three-dimensional cube) at the intersection of rows and columns. Each volume element may have a predetermined size, which may or may not be the same for all voxels in the voxel grid. If the input molecule is a drug molecule, the voxelized representation of the input molecule may include a voxel grid containing n×n×n voxels (e.g., 32×32×32 voxels, 64×64×64 voxels, etc.). In some cases, each voxel in the voxel grid may be associated with a value indicating the atomic density at the corresponding position. For example, a first voxel associated with a higher atomic density may be more likely to be part of an atom than a second voxel associated with a lower atomic density. It should be understood that the volume of an individual atom can extend across one or more voxels. In some cases, atomic density may be centered on an atom present in the input molecule, meaning that the atomic density of an individual atom spanning multiple voxels may be concentrated in the voxel containing the center of that atom. A voxel with an atomic density of 0 may be far from any atom in the input molecule, while a voxel with an atomic density of 1 may be at the center of an atom in the input molecule. Furthermore, in some cases, the voxelized representation of a molecule (e.g., the input molecule) may contain multiple channels, each corresponding to a type of atom that may be present in the input molecule. “Type of atom” can refer to the individual chemical elements in which the atom may exist. The voxelized representation may contain multiple channels, one for each type of atom present in the molecule, or at least one for each type of heavy atom. For example, in some cases, the voxelized representation of a molecule (e.g., an input molecule) may include a first channel corresponding to a first atomic type that may be present in the input molecule (e.g., a carbon (C) atom) and a second channel corresponding to a second atomic type that may be present in the input molecule (e.g., a nitrogen (N) atom).Each voxel in the first channel may be associated with a value representing the density of atoms of a first atomic type at the corresponding position, and each voxel in the second channel may be associated with a value representing the density of atoms of a second atomic type at the corresponding position. Thus, as will be described in more detail below, the molecular design calculation model may denoise the voxelized representation of the input molecule by, for example, updating the atomic density of at least one voxel in at least one channel of the voxelized representation of the input molecule across multiple sampling iterations. That is, in some cases, the term “denoising” refers to updating the voxelized representation of the input molecule, which may include updating the atomic density of at least one voxel in the voxelized representation of the input molecule. In some cases, updating the atomic density of a voxel in one channel of the voxelized representation of the input molecule may change the likelihood of the voxel, which is part of the atomic type associated with that channel.

[0082] In some exemplary embodiments, the molecular design computation model may denoise the input molecules (e.g., voxelized representations of the input molecules) across multiple sampling iterations, with each sampling iteration generating an updated voxelized representation different from the original input molecule's voxelized representation. In some cases, each updated voxelized representation may contain a sample selected from a data distribution of molecules (e.g., voxelized representations of molecules) exhibiting one or more desired properties. In this context, the term “data distribution” may refer to a collection of molecules with different molecular compositions and three-dimensional structures. Molecules exhibiting one or more desired properties may cluster in a high-density region of the data distribution, meaning that the molecular design computation model needs to sample each updated voxelized representation from this high-density region of the data distribution. However, this data distribution may be too high-dimensional to be directly approximated. For example, a normalization constant is needed to compute a probability density function (PDF) characterizing the probabilities of different molecules in the data distribution. In the case of molecular design, this normalization constant may correspond to the total number of molecules in the data distribution, which may be impossible to estimate. Therefore, in some cases, a molecular design computation model can be trained to approximate the data distribution by determining a function, such as a scoring function, that estimates the gradient (or change in density) across the data distribution. As will be described in more detail below, the molecular design computation model may use a function to induce sampling of updated voxelized representations from the data distribution, so that each successive sample is selected from an increasingly dense region of the data distribution.

[0083] As mentioned above, in some cases, denoising an input molecule across multiple sampling iterations may be equivalent to selecting a series of samples from a data distribution of the molecule (e.g., a data distribution of the voxelized representation of the molecule) where each sample corresponds to an updated voxelized representation different from that of the input molecule. For example, in some cases, the voxelized representation of the input molecule may be denoised by updating at least the atomic density of one or more voxels in at least one channel of the voxel grid forming the voxelized representation of the input molecule. In some cases, molecules in a high-density region of the data distribution may exhibit one or more desired properties, including drug-like properties such as affinity, specificity, biological activity, and suitability for development. Manipulating a three-dimensional representation of the input molecule, such as the voxelized representation of the input molecule, may increase the likelihood that the conformation (or three-dimensional structure) of the resulting output molecule is selected from a high-density region of the data distribution and therefore exhibits one or more desired properties.

[0084] In some cases, a molecular design model may be trained to approximate a data distribution by training the molecular design model with a training dataset of known molecules exhibiting one or more desired properties (e.g., PubChem datasets, QM9 molecular datasets, Geometric Ensemble of Molecules (GEOM) drug datasets, and / or similar). For example, in some cases, a molecular design model may be trained to approximate a data distribution by determining, at least, a function (e.g., a score function) that approximates different densities across the entire data distribution by Bayesian estimation. In some cases, the function may be parameterized by the molecular design model, meaning that the parameters of the function (e.g., a score function) are parameters of the molecular design model that have been tuned when the molecular design model is trained to approximate the data distribution. In some cases, high-density regions of the data distribution may be occupied by molecules similar to known molecules exhibiting one or more desired properties, while low-density regions of the data distribution may be occupied by molecules not similar to known molecules exhibiting one or more desired properties. The score function of the data distribution may represent transitions between different density regions of the data distribution, for example, transitions between high-density and low-density regions of the data distribution. Thus, once trained, the molecular design computation model may sample the data distribution based on the score function so that each consecutive sample (or molecule) is selected from an increasingly dense region of the data distribution.

[0085] In some exemplary embodiments, a molecular design computation model may be trained to denoise corrupted three-dimensional representations of known molecules from a training dataset and recover the original three-dimensional representations of the known molecules. For example, in some cases, a corrupted three-dimensional representation of a known molecule may be generated by corrupting the three-dimensional representation of the known molecule with noise (e.g., Gaussian noise such as isotropic Gaussian noise). Training a molecular design computation model may involve adjusting one or more parameters of the molecular design computation model (e.g., weights, biases, etc.) to reduce (or minimize) the difference (e.g., mean squared error (MSE)) between the recovered three-dimensional representation of the known molecule and the original three-dimensional representation of the known molecule.

[0086] In some exemplary embodiments, to avoid overfitting the molecular design model to known molecules in the training dataset, the molecular design model may be trained to recover a noisy version of the three-dimensional representation of the known molecules in the training dataset instead of the original three-dimensional representation. That is, the three-dimensional representation of each known molecule in the training dataset may be mixed with additional noise, but this noise should not be confused with noise that the molecular design model is trained to remove from the corrupted three-dimensional representation of each known molecule in the training dataset. In other words, in some cases, the molecular design model may be trained on a training dataset that includes noisy three-dimensional representations of known molecules and their corrupted versions. As will be described in more detail below, in some cases, the noisy three-dimensional representation of a known molecule may be generated by mixing the three-dimensional representation of the known molecule (e.g., a voxelized representation) with a first amount of noise (e.g., Gaussian noise such as isotropic Gaussian noise) to smooth the density of the data distribution of the known molecule while still maintaining at least some of the conformation (e.g., three-dimensional structure) of the known molecule, thereby obtaining the noisy representation of the known molecule. Subsequently, the noisy three-dimensional representation of a known molecule may be further corrupted by a second amount of noise (e.g., Gaussian noise such as isotropic Gaussian noise), generating a corrupted three-dimensional representation. In some cases, the molecular design calculation model may be trained to denoise the corrupted three-dimensional representation of the known molecule, for example by removing the second amount of noise, and to recover the noisy three-dimensional representation of the known molecule (which still contains the first amount of noise).Furthermore, in some cases, training of the molecular design computation model may include gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling), where the parameters of the molecular design computation model are adjusted over successive sampling iterations to increase the similarity (e.g., reduce the mean squared error (MSE)) between the three-dimensional representation of each known molecule recovered by the molecular design computation model from the corresponding corrupted three-dimensional representations of known molecules in the training dataset and the noisy three-dimensional representation of the sample molecules in the training dataset. The score function thus derived may capture a data distribution with smoother density transitions, which mitigates the phenomenon of mode collapse, where the molecular design computation model is not as robust and can only produce output molecules of a limited selection (e.g., those very close to known molecules in the data distribution).

[0087] As will be described in more detail below, during inference, a trained molecular design computation model may be applied to generate one or more output molecules by denoising the three-dimensional representation of an input molecule. In some cases, the input molecule may be a random molecule (e.g., a molecule in which the type and / or position of atoms are randomly selected) or a known molecule having one or more undesirable properties, meaning that the three-dimensional representation of the input molecule may contain at least some noise that needs to be removed so that the three-dimensional representation of the output molecule generated therefrom matches one or more desired properties. The molecular design computation model may do this by traversing the smoothed density of the noisy data distribution of the noisy three-dimensional representation of the molecule, for example, through one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo method) toward regions of incrementally higher density in the data distribution. Each iteration of gradient-based Markov chain Monte Carlo (MCMC) sampling may include updating the three-dimensional representation of the input molecule, which is equivalent to selecting the noisy three-dimensional representation of one or more molecules from different locations in the noisy data distribution. Even when selected from a noisy data distribution, the molecules corresponding to these noisy three-dimensional representations may be less distorted than the original three-dimensional representations of the input molecules. Such molecules corresponding to these noisy three-dimensional representations may better match molecules exhibiting one or more desired properties than the input molecules. In some cases, the noisy three-dimensional representations of molecules selected from a noisy data distribution may undergo further denoising to recover the corresponding molecules by mapping the noisy three-dimensional representation of each molecule from the noisy data distribution to the corresponding clean three-dimensional representation of the molecule in the true data distribution of molecules exhibiting one or more desired properties. It should be understood that sampling from a noisy data distribution may offer more advantages than sampling from the true data distribution of molecules exhibiting one or more desired properties.For example, sampling from a noisy data distribution of molecules exhibiting one or more desired properties that show smoother density transitions may be less affected by mode collapse than sampling from the true data distribution. In some cases, this may be because the noisy data distribution has fewer steep or abrupt gradients than the true data distribution, where steep gradients restrict sampling to the immediate vicinity of known molecules that characterize the true data distribution. In other words, molecular design computation models can produce outputs with limited diversity when sampling from the true data distribution (e.g., the aforementioned phenomenon called "mode collapse"), but sampling from a noisy distribution may increase the diversity of the model's output. Furthermore, sampling from a noisy data distribution occupied by noisy voxelized representations of molecules may offer additional advantages over sampling from a noisy data distribution occupied by noisy conventional three-dimensional representations of molecules, such as point cloud representations of molecules. For example, in some cases, molecular design computation models can be trained to operate with voxelized molecular representations and more easily generate drug-like molecules with greater efficacy, expressiveness, and scalability. Unlike working with conventional three-dimensional molecular representations (e.g., point cloud representations), working with voxelized molecular representations allows the disclosed molecular design calculation models to function without requiring the specification of the number of atoms present in the output molecule, and without workarounds to reconcile the discrete distribution of atom types with the continuous distribution of atomic positions associated with each molecule.

[0088] Despite the aforementioned advantages, working with voxelized molecular representations can impose a significant computational burden and can scale exponentially with molecular size (e.g., the number of constituent atoms). For example, a small molecule containing 10 heavy atoms already requires a [32×32×32] voxel grid with 32,000 features (or atomic density values) per molecule, but larger, more realistic drug-like molecules may require at least twice that size of voxel grid, with exponentially more points (e.g., a [64×64×64] voxel grid with 260,000 features (or atomic density values) per molecule). In some cases, applying molecular design computation models to work with voxelized representations of larger, more realistic drug-like molecules can be a challenging task, as is the case when training molecular design computation models on large training datasets (e.g., training datasets containing millions of voxelized representations of known molecules) to learn a wider variety of molecular spaces (or chemical spaces). Furthermore, even when candidate molecules are realistic and viable, a large portion of those generated by molecular design computation models may not be successfully synthesized in the laboratory. Therefore, it may be desirable to apply molecular design computation models to generate tens of thousands or even millions of candidate molecules. The computational load associated with generating molecules, especially larger or more numerous molecules, can be reduced by molecular design computation models that operate with low-dimensional embeddings of voxelized molecular representations. For example, in some cases, a molecular design computation model may be trained to generate output molecules by denoising the embedding of a three-dimensional representation of an input molecule. As will be described in more detail below, in some cases, a molecular design computation model may be trained on a training dataset containing corrupted embeddings of sample molecules exhibiting one or more desired properties, each generated by encoding a noisy three-dimensional representation (e.g., a voxelized representation) of one or more known molecules exhibiting a desired property before the resulting embedding is corrupted by the addition of noise (e.g., Gaussian noise such as isotropic Gaussian noise).

[0089] In some exemplary embodiments, encoding a three-dimensional representation of a molecule, such as a voxelized representation of a molecule, allows for the projection of the three-dimensional representation of a molecule (e.g., a voxelized molecular representation) from a higher-dimensional discrete space occupied by the three-dimensional representation of the molecule (e.g., a discrete voxelized space occupied by the voxelized molecular representation) to a lower-dimensional representation in a lower-dimensional latent space occupied by the corresponding molecular embedding. In other words, encoding a three-dimensional representation of a molecule, such as a voxelized representation of a molecule, can take a three-dimensional representation of a molecule in a higher-dimensional discrete space (e.g., a voxelized molecular representation) as input and produce a lower-dimensional representation of the molecule in a lower-dimensional latent space (i.e., a molecular embedding corresponding to the input three-dimensional representation) as output. Encoding a three-dimensional representation of a molecule, such as a voxelized representation of a molecule, can be performed using a machine learning model trained to identify latent space representations of the input molecule's three-dimensional representation from which the input molecule's three-dimensional representation can be recovered. In some cases, each embedding in the latent space may be a latent space representation of the corresponding voxelized representation of the molecule. Therefore, embeddings of a voxelized representation of a molecule may have different dimensions or features than the voxelized representation itself. For example, in some cases, encoding a voxelized representation of a molecule may reduce the dimensionality or amount of features present in the voxelized representation. Thus, the computational load of denoising a voxelized representation of a molecule to generate one or more output molecules from it can be reduced by a molecular design computation model that operates on the embedding of the voxelized representation of a molecule rather than the voxelized representation itself, because the embedding contains at least a smaller amount of features. Furthermore, in some cases, a molecular design computation model may be trained to approximate a noisy data distribution of one or more molecules exhibiting one or more desired properties, and one or more output molecules may be generated by sampling from there. This noisy data distribution, which may be occupied by the noisy embedding of the voxelized representation of a molecule, may exhibit smoother density transitions than the corresponding true data distribution.Thus, noisy data distributions may support more efficient sampling (e.g., via gradient-based Markov chain Monte Carlo (MCMC) sampling, such as Langevin-Markov chain Monte Carlo) methods, because they may exhibit fewer steep gradient changes that would otherwise hinder molecular design computation models from properly exploring the data distribution when sampling from them.

[0090] Figures 1A and 1B depict system diagrams showing different examples of molecular design system 100 according to several exemplary embodiments. Referring to Figures 1A and 1B, the molecular design system 100 may, in some cases, include a molecular design engine 110, a training engine 120, and a client device 130. In the examples of molecular design system 100 shown in Figures 1A and 1B, the molecular design engine 110, the training engine 120, and the client device 130 may be communicatively coupled via a network 140. The client device 130 may be a processor-based device including, for example, a workstation, desktop computer, laptop computer, smartphone, tablet computer, or wearable device. The network 140 may be a wired network and / or wireless network including, for example, a local area network (LAN), a virtual local area network (VLAN), a wide area network (WAN), a public land mobile network (PLMN), or the internet. In the example shown in Figures 1A and 1B, the molecular design calculation model 115 may include a denoising model 117 trained to generate an output molecule 162 by denoising at least the input molecule 152. The denoising model is a machine learning model trained to take a corrupted 3D representation of a molecule or its lower-dimensional embedding as input, where the corrupted 3D representation of a molecule is a noisy 3D representation of the molecule, and it generates the corresponding denoised 3D representation of a molecule or its lower-dimensional embedding as output, using training data containing 3D representations of several known molecules and their corresponding corrupted 3D representations. The known molecules in the training data may include several molecules exhibiting one or more desired properties. The denoising model may be an artificial neural network. The denoising model may be a deep learning model. The denoising model may be an encoder-decoder 3D convolutional neural network (CNN).For example, the molecular design calculation model 115 may, in some cases, apply a denoising model 117 to denoise the three-dimensional representation of the input molecule 152, or perform an embedding 154 of the three-dimensional representation of the input molecule 152, in order to generate the output molecule 162. In some cases, the denoising model 117 may denoise the three-dimensional representation of the input molecule 152 (or its embedding 154) over multiple consecutive sampling iterations, so that some of the noise present in the three-dimensional representation of the input molecule 152 (or its embedding 154) is removed at each sampling iteration.

[0091] As will be explained in more detail below, denoising the three-dimensional representation of the input molecule 152 can alter the composition and / or conformation (or three-dimensional structure) of the input molecule 152 so that the composition and conformation (or three-dimensional structure) of the resulting output molecule 162 matches the composition and conformation (or three-dimensional structure) of a molecule exhibiting one or more desired properties. If the output molecule 162 is a drug molecule, for example, one or more desired properties may include drug-like properties such as affinity, specificity, biological activity, and suitability for development. In some cases, whether the output molecule 162 exhibits a particular desired property may depend on whether the output molecule 162 exhibits the corresponding conformation (or three-dimensional structure). Therefore, in some cases, a molecular design calculation model 115 that applies the denoising model 117 to a three-dimensional representation of the input molecule 152 (or its embedding 154) instead of a one-dimensional or two-dimensional representation of the input molecule 152 increases the likelihood that the resulting output molecule 162 exhibits a conformation (or three-dimensional structure) that matches one or more desired properties.

[0092] In some exemplary embodiments, the molecular design computation model 115, including a denoising model 117, may be trained to learn or approximate a data distribution of molecules exhibiting one or more desired properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development). For example, in some cases, the molecular design computation model 115 may be trained to approximate a data distribution of molecules exhibiting one or more desired properties based on a training dataset of known molecules exhibiting one or more desired properties (e.g., PubChem dataset, QM9 molecular dataset, Geometric Ensemble of Molecules (GEOM) drug dataset, and / or similar). As will be described in more detail below, the molecular design computation model 115 may also be trained to approximate a noisy data distribution, which is comprised of noisy three-dimensional representations of known molecules exhibiting one or more desired properties. Furthermore, the molecular design calculation model 115 may be trained to operate in either a discrete space occupied by three-dimensional representations of molecules exhibiting one or more desired properties (e.g., voxelized representations), or a latent space occupied by embeddings of three-dimensional representations of molecules that are lower-dimensional representations of molecules (e.g., embeddings of voxelized representations).

[0093] To further illustrate, Figure 1A shows an example of the molecular design engine 110, where the molecular design calculation model 115 is trained to operate in discrete space (three-dimensional voxelized representation), whereas the molecular design calculation model 115 included in the example of the molecular design engine 110 shown in Figure 1B may be trained to operate in latent space. The latent space may contain continuous values ​​(embeddings) of multiple features. In either example of the molecular design engine 110, the molecular design calculation model 115 may be trained to approximate a noisy data distribution by being trained, for example, on a noisy three-dimensional representation of a molecule exhibiting one or more desired properties. For example, the example of the molecular design calculation model 115 shown in Figure 1A may be trained to approximate a noisy discrete distribution occupied by a noisy three-dimensional representation of a molecule, while the example of the molecular design calculation model 115 shown in Figure 1B may be trained to approximate a noisy latent distribution occupied by a noisy embedding of a three-dimensional representation of a molecule.

[0094] Referring first to Figure 1A, the molecular design engine 110 may, in some cases, include a molecular design calculation model 115 and a recovery model 118. Alternatively, Figure 1B shows another example of the molecular design engine 110, which may also include an encoder 111 and a decoder 119 in addition to the molecular design calculation model 115 and the recovery model 118. In some cases, the molecular design engine 110 may apply the molecular design calculation model 115 to generate an output molecule 162 based on at least an input molecule 152. For example, in the example of the molecular design engine 110 shown in Figure 1A, the molecular design calculation model 115 may operate in a three-dimensional representation of the input molecule 152, which may be a voxelized representation of the input molecule 152. In doing so, the molecular design calculation model 115 may operate in a discrete voxelized space occupied by noisy voxelized representations of different molecules (e.g., molecules exhibiting one or more desired properties). Alternatively, in the example of the molecular design engine 110 shown in Figure 1B, the molecular design calculation model 115 may operate on an embedding 154 of the input molecule 152. As will be described in more detail below, the embedding 154 of the input molecule 152 may be generated by an encoder 111 that encodes a three-dimensional representation (e.g., a voxelized representation) of the input molecule 152. In this modification of the molecular design engine 110, the molecular design calculation model 115 may operate in a latent space occupied by noisy embeddings of three-dimensional representations (e.g., voxelized representations) of different molecules.

[0095] In some exemplary embodiments, the molecular design calculation model 115 may include a denoising model 117 trained to denoise a three-dimensional representation of an input molecule 152 based on a function 175, such that the resulting three-dimensional representation of an output molecule 162 is sampled from a high-density region of the data distribution of one or more molecules exhibiting desired properties. Figure 1A shows an example of a denoising model 117 trained to denoise a three-dimensional representation of an input molecule 152, and Figure 1B shows another example of a denoising model 117 trained to denoise an embedding 154 of the three-dimensional representation of the input molecule 152. In some cases, the denoising model 117 may denoise the three-dimensional representation of the input molecule 152 (e.g., a voxelized representation of the input molecule 152) or its embedding 154 over a plurality of time steps. In some cases, the denoising performed at each time step may be equivalent to selecting one or more samples (e.g., intermediate molecules) from different locations in the data distribution. In some cases, function 175 may be a scoring function that outputs a value (e.g., a score) indicating a local density change at a specific location in the data distribution (e.g., the location occupied by a particular molecule). Thus, denoising of the input molecules 152 may be performed based on the output of the scoring function so that each successive sample (or molecule) is selected from an increasingly dense region of the data distribution.

[0096] In some exemplary embodiments, denoising of the input molecule 152 may include updating the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 (or its embedding 154) that can represent the composition and conformation (or three-dimensional structure) of the input molecule 152, in order to increase the likelihood that the resulting output molecule 162 is in a data distribution of molecules exhibiting one or more desired properties. In some cases, the molecular design calculation model 115 may apply a denoising model 117 to modify the three-dimensional representation of the input molecule 152 (or its embedding 154) over one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Markov chain Monte Carlo (MCMC) using Langevin dynamics, for example). For example, in some cases, each iteration of gradient-based Markov chain Monte Carlo (MCMC) sampling may include selecting a sample (or molecule) from the data distribution that includes one or more modifications to the three-dimensional representation of the input molecule 152 (or its embedding 154). As mentioned above, in some cases, sampling from the data distribution may be guided by function 175 (e.g., a score function). For example, if function 175 is a score function, function 175 may output a value (e.g., a score) for each sample (or numerator) selected from the data distribution that corresponds to the change in density observed at the location in the data distribution occupied by the sample (or numerator). Thus, in some cases, sampling from the data distribution may be guided by a function such that consecutive samples are selected from a gradually increasing density region of the data distribution.

[0097] To elaborate further, in some cases, the denoising model 117 may be applied to update the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 (or its embedding 154) by, for example, selecting at least a first sample and a second sample from the data distribution. It should be understood that each of the first and second samples may correspond to the modified three-dimensional representation of the input molecule 152 in the example shown in Figure 1A, or, in the case of Figure 1B, to the modified embedding of the three-dimensional representation of the input molecule 152. If function 175 is a scoring function, function 175 may assign a first value (e.g., a first score) to the first sample that indicates a more positive local change (e.g., an increase or a smaller decrease) in the density of the data distribution at a first location in the first sample, and a second value to the second sample that indicates a less positive local change (e.g., a smaller increase or decrease) in the density of the data distribution at a second location in the second sample. In some cases, the molecular design calculation model 115 may apply a denoising model 117 to further modify the first sample in order to sample the third sample from a region of higher density in the data distribution than the first and second samples, thereby selecting a third sample (e.g., another modified three-dimensional representation or another modified embedding) from the data distribution.

[0098] In some exemplary embodiments, the molecular design calculation model 115 may apply a denoising model 117 to denoise the voxelized representation of the input molecule 152 (or its embedding 154) instead of a conventional three-dimensional representation of the input molecule 152, such as a point cloud representation of the input molecule 152. For example, in some cases, the voxelized representation of the input molecule 152 may represent the types and locations of atoms present in the input molecule 152 as a continuous (e.g., Gaussian) density across a three-dimensional voxel grid. To indicate the locations of atoms present in the input molecule 152, each voxel in the voxel grid may be associated with a value indicating the atomic density at the corresponding location. In some cases, the atomic density associated with a particular voxel in the voxel grid may correspond to the likelihood that that voxel is part of the atoms at that location. For example, a first voxel with a higher atomic density may be more likely to be part of the atoms forming the input molecule 152 than a second voxel with a lower atomic density. Therefore, the voxelized representation of the input molecule 152 may represent the positions of atoms that distinguish the input molecule 152 based on the atomic density associated with each voxel in the voxel grid, between voxels in the voxel grid that form part of the atoms in the input molecule 152 and voxels in the voxel grid that do not form part of the atoms in the input molecule 152. In some cases, the atoms that form the input molecule 152 may be located at voxel locations associated with atomic densities that satisfy one or more thresholds.

[0099] In some exemplary embodiments, the voxelized representation of the input molecule 152 may include one or more channels, each corresponding to a type of atom that may be present in the input molecule 152. For example, in some cases, the voxelized representation of the input molecule 152 may include a separate channel for each type of heavy atom that may be present in the input molecule 152. Including separate channels for different types of atoms in the voxelized representation of the input molecule 152 can avoid the discrete distribution typically associated with atom types seen in conventional three-dimensional representations (e.g., point cloud representations). Instead, the voxelized representation of the input molecule 152 may represent the types and locations of atoms in the input molecule 152 as one or more continuous (e.g., Gaussian) densities across the aforementioned three-dimensional voxel grid. For example, the voxelized representation of the input molecule 152 may include a first channel representing a first type of atom that may be present in the input molecule 152 (e.g., carbon C atoms). The presence of the input molecule 152 and the first type of atoms at each of their locations can be represented by a first continuous (e.g., Gaussian) density across the first channel in the voxelized representation of the input molecule 152. Note that the density is continuous in the sense that the values ​​associated with each voxel can take continuous values ​​(e.g., values ​​within a continuous, bounded, or unbounded distribution). In some cases, the voxelized representation of the input molecule 152 may further include a second channel representing a second type of atom (e.g., nitrogen (N) atoms) that may be present in the input molecule 152. The presence of the second type of atom and each of their locations can be represented by a second continuous (e.g., Gaussian) density across the second channel in the voxelized representation of the input molecule.

[0100] Unlike conventional three-dimensional representations of the input molecule 152 (e.g., point cloud representations) that represent the types and positions of atoms within the input molecule 152 as two distinct types of distributions (e.g., discrete distributions of atom types and continuous distributions of atom positions), the voxelized representation of the input molecule 152 can represent the types and positions of atoms within the input molecule 152 together as one or more continuous (e.g., Gaussian) distributions in the manner described above. Thus, the molecular design calculation model 115 can manipulate the voxelized representation of the input molecule 152 by applying the denoising model 117 without workarounds to harmonize the two distinct types of distributions required for the conventional three-dimensional representation of the input molecule 152. The voxelized representation of the input molecule 152 can also represent the conformation (or three-dimensional structure) of the input molecule 152 better than the conventional three-dimensional representation of the input molecule 152. For example, the voxelized representation of the input molecule 152 can capture long-range dependencies between distant atoms, even when the input molecule 152 contains a large number of atoms. Furthermore, the molecular design calculation model 115 can apply the denoising model 117 to denoise the voxelized representation of the input molecule 152 and generate the output molecule 162 without prior knowledge of the amount of molecules present in the output molecule 162.

[0101] In some exemplary embodiments, the training engine 120 may be trained to generate one or more training samples to be included in the training dataset. Figure 1A shows an example of the training engine 120, in which the corrupted engine 121 generates each training sample by adding noise (e.g., Gaussian noise such as isotropic Gaussian noise) to a noisy three-dimensional representation 182 of the sample molecule (e.g., a known molecule exhibiting one or more desired properties), thereby generating a corrupted three-dimensional representation 184 of the sample molecule. The corrupted engine 121 may add noise to the already noisy three-dimensional representation 182 of the sample molecule so that the molecular design calculation model 115 is trained to approximate the noisy data distribution of the molecule exhibiting one or more desired properties, and it should be understood that this has smoother density transitions than the true data distribution of the molecule exhibiting one or more properties. Therefore, in some cases, the molecular design calculation model 115, including a denoising model 117, may be trained to denoise the corrupted three-dimensional representation of the sample molecule and, for each training sample, recover the corresponding noisy three-dimensional representation of the sample molecule rather than a clean (or original) three-dimensional representation of the sample molecule. Doing so may be equivalent to sampling from a noisy data distribution of molecules exhibiting one or more desired properties, rather than from the true distribution of molecules.

[0102] Alternatively, Figure 1B shows another example of the training engine 120 in which the encoder 111 first encodes the noisy three-dimensional representation 182 of the sample molecule and generates its embedding 186 before the corruption engine 121 adds noise to generate a corrupted embedding 188 of the noisy three-dimensional representation 182 of the sample molecule. In this modification of the molecular design engine 110, the molecular design computation model 115 may be trained to approximate a noisy latent distribution of noisy embeddings of the noisy three-dimensional representations of molecules exhibiting one or more desired properties, instead of the noisy but discrete distribution that the molecular design computation model 115 is trained to approximate in the example shown in Figure 1A. To achieve this result, the training engine 120 may generate each training sample in the training dataset to include the corrupted embedding 188. For example, Figure 1B shows that the training engine may further include an encoder 111, which can first encode a noisy three-dimensional representation 182 of a sample molecule (e.g., a known molecule exhibiting one or more desired properties) to generate an embedding 186 before the corrupted engine 121 adds noise to it to generate a corrupted embedding 188. In some cases, a molecular design calculation model 115 including a denoising model 117 may be trained to denoise the corrupted embedding 188 and recover the embedding 186 from it. The denoising model 117, the encoder 111, and the corresponding decoder may be trained together.

[0103] In some exemplary embodiments, training the molecular design calculation model 115 may include adjusting one or more parameters (e.g., weights, biases, etc.) of the denoising model 117. In the example shown in Figure 1A, the parameters of the denoising model 117 may be adjusted so that the denoising model 117 can recover the corresponding noisy three-dimensional representation 182 of the sample molecule from the corrupted three-dimensional representation 184 of the sample molecule. For example, as will be described in more detail below, one or more parameters of the denoising model 117 may be adjusted over multiple iterations to increase (or maximize) the similarity (e.g., to reduce (or minimize) the mean squared error (MSE)) between the noisy three-dimensional representation 182 of the sample molecule recovered by the denoising model 117 from the corrupted three-dimensional representation 184 of the sample molecule and the original noisy three-dimensional representation 182 of the sample molecule. Alternatively, the example in Figure 1B shows that the parameters of the denoising model 117 can be adjusted so that the denoising model 117 can recover the embedding 186 generated by encoding the noisy three-dimensional representation 182 of the sample molecule from the corrupted embedding 188. For example, in the example shown in Figure 1B, the parameters of the denoising model 117 can be adjusted to increase (or maximize) the similarity between the embedding 186 recovered by the denoising model 117 from the corrupted embedding 186 and the original uncorrupted embedding 186 of the three-dimensional representation 182 of the sample molecule (e.g., reducing (or minimizing) an arbitrary loss function that quantifies the difference between the embedding 186 recovered by the denoising model 117 from the corrupted embedding 188 and the original uncorrupted embedding 186 of the three-dimensional representation 182 of the sample molecule, e.g., reducing (or minimizing) the mean squared error (MSE).

[0104] In some exemplary embodiments, training the molecular design computation model 115 may include determining a function 175 that can be parameterized by parameters (e.g., weights, biases, etc.) of a denoising model 117. For example, training the molecular design computation model 115, which may include tuning one or more parameters of the denoising model 117, may determine the function 175 (e.g., a score function) by tuning at least the corresponding parameters of the function 175. In some cases, the function 175 may approximate different densities across a data distribution of molecules exhibiting one or more desired properties, where molecules exhibiting one or more properties are more likely to occupy high-density regions of the data distribution. In the example shown in Figure 1A, this data distribution may be a noisy data distribution occupied by noisy three-dimensional representations of molecules. Alternatively, in the example of the molecular design engine 110 shown in Figure 1B, this data distribution may be a noisy latent distribution occupied by noisy embeddings of three-dimensional representations of molecules.

[0105] As described above, in some exemplary embodiments, overfitting of the molecular design computation model 115, including the denoising model 117, to known molecules in the training dataset can be avoided by training the denoising model 117 to approximate a noisy data distribution occupied by noisy three-dimensional representations of molecules, such as noisy voxelized representations. An example of this training dataset is shown in Figure 1A, where the molecular design computation model 115 is trained to recover noisy three-dimensional representations 182 of sample molecules, rather than clean (or original) three-dimensional representations of sample molecules. Once trained, as will be described in more detail below, the molecular design computation model 115 can generate a three-dimensional representation of an output molecule 158 by traversing (i.e., iteratively sampling different regions below) the smoothed density of the noisy data distribution and sampling at least one updated three-dimensional representation 160. The noisy data distribution may be occupied by noisy three-dimensional representations of molecules exhibiting one or more desired properties. Therefore, the updated three-dimensional representation 160 may contain at least some noise that can be removed by denoising the updated three-dimensional representation 160 by applying the recovery model 118. The recovery model 118 may be a machine learning model trained to take a noisy three-dimensional representation 160 of a molecule as input and produce a corresponding denoised three-dimensional representation as output. In doing so, a three-dimensional representation of the output molecule 162 may be produced, which occupies the true data distribution of clean three-dimensional representations of molecules exhibiting one or more desired properties.

[0106] Alternatively, Figure 1B shows another example of the molecular design engine 110 in which the molecular design calculation model 115 is trained to approximate a noisy latent distribution occupied by embeddings of noisy three-dimensional representations of molecules exhibiting one or more desired properties. In this modification of the molecular design calculation model 115, the denoising engine 117 may be trained to recover the embedding 186 of the noisy three-dimensional representation 182 of the sample molecule from the corrupted embedding 188. Once trained, the molecular design calculation model 115 may apply the denoising model 117 to denoise the embedding 154 generated by the encoder 111 encoding the three-dimensional representation of the input molecule 152. Denoising may include updating the embedding 154 over multiple consecutive sampling iterations to generate at least one updated embedding 156 during each sampling iteration. Doing so may be equivalent to the molecular design calculation model 115 selecting a sample from the noisy latent distribution, and the molecular design calculation model 115 may continue to select a sample from there until one or more criteria are met. In some cases, the updated embedding 156 may be decoded by, for example, a decoder 119 before the resulting noisy three-dimensional representation 158 is denoised by the recovery model 118 in order to generate a three-dimensional representation of the output molecule 162. As will be described in more detail below, in this example of the molecular design engine 110, the molecular design calculation 115 may operate in a noisy latent space occupied by noisy embeddings of the three-dimensional representation of the molecule, rather than in the noisy three-dimensional representation found in a discrete voxelized space. Furthermore, it should be understood that although the denoising model 117 and the recovery model 118 may in some cases share the same architecture (e.g., an artificial neural network (ANN)), the two models are trained to denoise different things. For example, the denoising model 117 may be trained to denoise the three-dimensional representation of the input molecule 152 or its embedding 154 so that the resulting three-dimensional representation of the output molecule 162 matches the composition and / or conformation of a molecule exhibiting one or more desired properties (e.g., drug-like properties).In contrast, the recovery model 118 can be trained to remove noise that is added to smooth the density of known molecules available for training the molecular design calculation model 115.

[0107] Referring again to Figure 1B, the embedding 154 of the three-dimensional representation of the input molecule 152 can be generated by the encoder 111 which encodes the three-dimensional representation of the input molecule 152. In some cases, the embedding 154 may be a lower-dimensional representation of the three-dimensional representation of the input molecule 152 generated by the encoder 111 which reduces the dimensionality of the three-dimensional representation of the input molecule 152. For example, in some cases, the encoder 111 and decoder 119 may form an autoencoder including, for example, a variational autoencoder (VAE) such as a vector quantized variational autoencoder (VQ-VAE). The encoder 111 can generate the embedding 154 by reducing the dimensionality of at least the three-dimensional representation of the input molecule 152 (e.g., a voxelized representation). In this regard, reducing the dimensionality of the three-dimensional representation of the input molecule 152 may involve downsampling, compressing, or reducing the dimensionality of the three-dimensional representation of the input molecule 152 by condensing at least some of the features (e.g., atomic density values) present in the three-dimensional representation of the input molecule 152, such that the resulting embedding 154 contains fewer features than the original three-dimensional representation of the input molecule 152, but those features still capture the same (or similar) information conveyed in the original three-dimensional representation of the input molecule 152. In the case of a voxelized representation of the input molecule 152, each feature present therein may correspond to an atomic density value associated with each voxel contained in the voxel grid representing the input molecule 152. For example, if the voxelized representation of the input molecule 152 contains a [32 × 32 × 32] voxel grid, the voxelized representation of the input molecule 152 may contain 32,000 features (or atomic density values). At least some of these 32,000 features may be condensed by the encoder 111 when generating the embedding 154. In this way, the embedding 154 may contain fewer features, such as 4 × 4 × 4 = 64 features for the denoising model 117 to operate when generating the output molecule 162.

[0108] As mentioned above, the embedding 154 of the three-dimensional representation of the input molecule 152 shown in Figure 1B may contain fewer features than the original three-dimensional representation of the input molecule 152. Furthermore, the embedding 154 may be generated by an encoder 111 that downsamples, compresses, or reduces the dimension of the three-dimensional representation of the input molecule 152. Doing so may be equivalent to an encoder 111 that maps the three-dimensional representation of the input molecule 152 from a high-dimensional discrete voxelized space to a low-dimensional latent space. In some cases, the molecular design calculation model 115 (e.g., denoising engine 117) may denoise the embedding 154, for example, over one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling. During each iteration of gradient-based Markov Monte Carlo (MCMC) sampling, the molecular design calculation model 115 (e.g., denoising model 117) may sample at least one updated embedding 156 from this low-dimensional latent space. The fact that embedding 154 may contain orders of magnitude fewer features than the original three-dimensional representation of the input molecule 152 means that the molecular design computation model 115 can apply the denoising model 117 to generate the output molecule 162 by operating on embedding 154 faster and with higher computational efficiency, while achieving equivalent or better performance qualitatively and quantitatively. This can be particularly advantageous in applications such as computational drug design, which require the generation of a large number of candidate molecules in a short time. In some cases, by reducing the dimensionality of the original three-dimensional representation of the input molecule 152, the denoising model 117 can operate on and generate larger molecules (e.g., molecules containing more than 200 atoms) and larger numbers of molecules.

[0109] In some cases, the compactness of the embedding 154 relative to the three-dimensional representation of the input molecules 152 also means that fewer computational resources are required when operating on the embedding 154. For example, to operate directly on the three-dimensional representation of the input molecules 152 (e.g., a [32×32×32] voxel grid with 32,000 features), the denoising model 117 may be implemented to include a large number of trainable parameters (e.g., 100 million parameters). Conversely, if the denoising model 117 is applied to operate on the embedding 154 instead, the denoising model 117 can be implemented with far fewer trainable parameters. Implementing the denoising model 117 with fewer parameters can improve the performance of the denoising model 117, as a large number of parameters can reduce the generalizability of the denoising model 117. For example, if the denoising model 117 includes a large number of features but has relatively few known molecules available to train it, the denoising model 117 may be particularly prone to overfitting. If the denoising model 117 is overfitted to known molecules in the training dataset, that is, if the denoising model 117 is sufficiently trained on the training dataset (i.e., trained to learn a data distribution that is overly concentrated around molecules in the training dataset), then the denoising model 117 may not be able to generalize. In this context, generalization refers to the ability to accurately denoise input molecule 152 if it is not one of the known molecules in the training dataset. Therefore, overfitting the denoising model 117 can prevent it from accurately denoising molecules that are not any of the known molecules in the training data.

[0110] Referring again to Figure 1B, in the example of the molecular design engine 110 shown therein, the updated embedding 156 generated by sampling from the latent voxelized space can be decoded by the decoder 119 before the resulting noisy three-dimensional representation 158 is denoised by the recovery engine 118. The decoding performed by the decoder 119 may map the updated embedding 156 from the latent space to the discrete space, while the subsequent denoising performed by the recovery model 118 may constitute a jump from the noisy data distribution to the true data distribution of the molecule. For example, between each iteration of a gradient-based Markov chain Monte Carlo (e.g., Langevin-Markov chain Monte Carlo), the molecular design calculation model 115 may apply a denoising model 117 to sample from a noisy latent distribution of molecules exhibiting one or more desired properties. Sampling from the noisy latent distribution in this context may include updating the embedding 154 of the three-dimensional representation (e.g., the voxelized representation) of the input molecule 152. Doing so may be equivalent to selecting from the data distribution at least one updated embedding 156 that is decoded by the decoder 119 before being denoised by the recovery model 118 to generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162. As will be described in more detail below, the molecular design calculation model 115 may further update the noisy embedding 156, for example, over multiple iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling, until one or more criteria are met.

[0111] If one or more criteria are met, the molecular design engine 110 may recover the output molecule 162 based on at least a three-dimensional representation of the output molecule 162. For example, in some cases, the molecular design engine 110 may recover the positions (e.g., coordinates) of atoms present in the output molecule 162 and one or more bonds between them, based on at least a three-dimensional representation of the output molecule 162. The recovery of the positions of atoms present in the output molecule 162 is performed by identifying the maximum value (e.g., peak) of the predicted density contained in the three-dimensional representation of the output molecule 162. In doing so, the molecular design engine 110 may determine alternative representations of the output molecule 162, including, for example, a one-dimensional representation of the output molecule 162 (e.g., a Simplified Molecular Input Line Input System (SMILES) string) and a two-dimensional representation of the output molecule 162 (e.g., a molecular graph). It should be understood that the output molecule 162 thus generated may be more likely to exhibit one or more desired properties of the molecule in the data distribution. In particular, the denoising model 117 may generate the output molecule 162 to exhibit a composition and / or stereostructure (or three-dimensional structure) that matches one or more desired properties. By manipulating the embedding 154 of the three-dimensional representation (e.g., a voxelized representation) of the input molecule 152, the denoising model 117 may generate the output molecule 162 faster and with less computational load.

[0112] As described above, in some exemplary embodiments, the molecular design calculation model 115 may be trained to recover a noisy three-dimensional representation 182 of a sample molecule (e.g., a noisy voxelized representation of the sample molecule) that is generated by adding noise (e.g., Gaussian noise such as isotropic Gaussian noise) to the three-dimensional representation of the sample molecule. In the example shown in Figure 1A, the molecular design calculation model 115 may be trained to denoise a corrupted three-dimensional representation 184 of the sample molecule by at least correcting the corrupted three-dimensional representation 184 of the sample molecule in order to recover the noisy three-dimensional representation 184 of the sample molecule. Alternatively, Figure 1B shows an example of a molecular design engine 110 in which the molecular design calculation model 115 is trained to recover an embedding 186 of the noisy three-dimensional representation 182 of the sample molecule. As shown in Figure 1B, in some cases, the molecular design calculation model 115 may denoise the corrupted embedding 188 by correcting at least the corrupted embedding 188, which may be generated by a corruption engine 121 that adds noise (e.g., Gaussian noise) to the embedding 184 of the three-dimensional representation 182 of the sample molecule. As previously mentioned, the embedding 184 may be generated by the encoder 111 by downsampling or reducing the dimension of the noisy three-dimensional representation 182 (e.g., a noisy voxelized representation) of the sample molecule. However, as previously mentioned, downsampling of the noisy three-dimensional representation 182 (e.g., a noisy voxelized representation) of the sample molecule may be optional, and this may be the case if the encoder 111 implements an identity function. Thus, in some cases, the embedding 184 may contain the same amount of features as the original noisy three-dimensional representation 182 (e.g., a noisy voxelized representation) of the sample molecule. In those cases, the embedding 154 can capture the same information present in the original three-dimensional representation (e.g., voxelized representation) of the input molecule 152 without the condensation of the features present therein. In other words, encoding the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 can be an arbitrary operation, even if the example molecular design system 100 shown in Figure 1B includes an encoder 111.

[0113] Figure 2 shows a flowchart illustrating an example of a process 200 for machine learning-ready generation of three-dimensional molecules in voxelized space according to several exemplary embodiments. Referring to Figures 1A-1B and 2, the process 200 may be performed by a molecular design engine 110 to generate an output molecule 162 by training and applying a molecular design computation model 115 to denoise a three-dimensional representation, such as a voxelized representation, of at least an input molecule 152. For example, in some cases, the molecular design computation model 115 may be trained on a noisy three-dimensional representation 182 of a sample molecule, which is generated by adding noise to the original three-dimensional representation of the sample molecule, so that the molecular design computation model 115 is trained to approximate a noisy data distribution with smoother density transitions. Figure 1A shows one variation in which the molecular design computation model 115 is trained on a corrupted three-dimensional representation 184 of the sample molecule, which may be generated by adding additional noise to the noisy three-dimensional representation 182 of the sample molecule without any downsampling or compression. Alternatively, Figure 1B shows another variation in which the molecular design calculation model 115 is trained on a corrupted embedding 186 of a noisy three-dimensional representation 182 of the sample molecule. This corrupted embedding 188 may also be generated by adding noise to the embedding 154 of the noisy three-dimensional representation 182 of the sample molecule, which is generated by an encoder 111 that downsamples (or compresses) features present in the noisy three-dimensional representation 182 of the sample molecule (e.g., a noisy voxelized representation). In other words, it should be understood that the molecular design calculation model 115 can be trained to operate in either a noisy discrete voxelized space occupied by a noisy three-dimensional representation of the molecule, or alternatively, a noisy latent voxelized space occupied by an embedding of a noisy three-dimensional representation of the molecule.

[0114] In 202, the training engine 120 may generate a training set containing multiple corrupted sample molecules. In some exemplary embodiments, generating a training dataset may involve the training engine 120 generating a training dataset containing multiple corrupted sample molecules. This training dataset can then be used to train the molecular design calculation model 115 to approximate a data distribution of molecules exhibiting one or more desired properties (e.g., drug-like properties). In some cases, each corrupted sample molecule may be a noisy three-dimensional representation of a known molecule that has been further corrupted with additional noise (e.g., Gaussian noise such as isotropic Gaussian noise). For example, Figure 1A shows an example of this, where the corruption engine 121 generates a corrupted three-dimensional representation 184 of a sample molecule by adding additional noise to a noisy three-dimensional representation 182 of the sample molecule. As will be described in more detail below, the molecular design calculation model 115 (e.g., denoising model 117) may be trained to approximate a noisy data distribution with smoother density transitions by being trained to recover a noisy three-dimensional representation 182 of a sample molecule from a corrupted three-dimensional representation 184 of the sample molecule. Alternatively, Figure 1B shows another example in which the training engine 120 generates each corrupted sample molecule in the training dataset, including a corrupted embedding of the noisy three-dimensional representation 182 of the sample molecule. For example, in some cases, the corruption engine 121 may generate a corrupted embedding 188 by adding noise (e.g., Gaussian noise such as isotropic Gaussian noise) to the embedding 186 of the noisy three-dimensional representation 182 of the sample molecule (e.g., a noisy voxelized representation). In some cases, the training engine 120 may further enhance the training dataset by applying one or more transformations to the noisy three-dimensional representation 182 of the sample molecule (e.g., a voxelized representation), including, for example, translation (e.g., by shifting the center of the sample molecule in each of the three dimensions by sampling a uniform shift), rotation (e.g., by uniformly sampling three Euler angles), and reflection.

[0115] The occurrence of overfitting and mode collapse may be mitigated by training the molecular design calculation model 115 on a noisy three-dimensional representation 182 of sample molecules, which typically involves training the molecular design calculation model 115 on a high-dimensional data distribution (e.g., 10) based on a disproportionately small number of known molecules (e.g., PubChem dataset, QM9 molecular dataset, Geometric Ensemble of Molecules (GEOM) drug dataset and / or similar). 60 This occurs when the system is trained to approximate the molecular space of a given chemical compound.

[0116] In the example of the molecular design calculation model 115 shown in Figures 1A-1B, the molecular design calculation model 115 may include a denoising model 117. In this case, training the molecular design calculation model 115 may include training the denoising model 117 to approximate a noisy data distribution, or possibly a noisy latent distribution, either of which exhibits smoother density transitions and is more efficient to sample than the true data distribution. In some cases, the denoising model 117 may be an artificial neural network (ANN), in which case training the denoising model 117 may include tuning one or more parameters of the ANN (e.g., weights, biases, etc.). By doing so, the parameters of function 175 may also be determined such that function 175 outputs values ​​indicating the likelihood that molecules exhibiting one or more desired characteristics are located at specific locations within the data distribution. For example, in some cases, function 175 may be a score function whose output is a value (e.g., a score) that indicates transitions between different density regions of the data distribution, including transitions between high-density regions that are more likely to be occupied by molecules exhibiting one or more desired properties and low-density regions of the data distribution that are less likely to be occupied by molecules exhibiting one or more desired properties. In some cases, the denoising model 117 may be trained to recover noisy three-dimensional representations 182 of sample molecules or embeddings 186 in order to avoid overfitting the denoising model 117 to a relatively small number of known molecules in the training dataset available to characterize the data distribution, for example.

[0117] To explain further, TIFF2026518674000001.tif6170 shows the true data distribution of voxelized representations of molecules exhibiting one or more desired properties. TIFF2026518674000002.tif6170 represents the corresponding noisy data distribution, and this data distribution shows a smoother energy landscape, while the unknown data distribution It may be possible to sample more efficiently than TIFF2026518674000003.tif6170. In some cases, the true data distribution TIFF2026518674000004.tif6170 may be unknown, and this is because the denoising model 117 trains on a known molecular training dataset from the true data distribution. This means it can be trained to approximate TIFF2026518674000005.tif6170. To avoid overfitting the denoising model 117 to the training dataset, the denoising model 117 instead trains to approximate the noisy data distribution It can be trained to approximate TIFF2026518674000006.tif6170. In some cases, noisy data distributions may be present. TIFF2026518674000007.tif6170 is the true data distribution TIFF2026518674000008.tif6170 has known covariances This may be obtained by convolving with a Gaussian kernel (e.g., an isotropic Gaussian kernel) that has TIFF2026518674000009.tif7170. Doing so would reveal the true data distribution. TIFF2026518674000010.tif6170 (for example) TIFF2026518674000011.tif6170 Here, TIFF2026518674000012.tif6170, Voxelized molecular representation from TIFF2026518674000013.tif7170) Noise in TIFF2026518674000014.tif3170 Adding TIFF2026518674000015.tif3170 improves the representation of noisy voxelized molecules. This may be equivalent to generating TIFF2026518674000016.tif4170. Considering the above formula, a noisy voxelized molecular representation TIFF2026518674000017.tif4170 is a noisy data distribution as shown below. It can be sampled from TIFF2026518674000018.tif6170.

number

[0118] This is the true data distribution When converting TIFF2026518674000020.tif6170, noise is generated. A clean (or original) voxelized representation without TIFF2026518674000021.tif3170 added. While still retaining some of the structural information present in TIFF2026518674000022.tif3170, the true data distribution The density of TIFF2026518674000023.tif6170 can be smoothed. Clean voxelized molecular representation. Noise added to TIFF2026518674000024.tif3170 If TIFF2026518674000025.tif3170 is Gaussian (e.g., isotropic Gaussian), then it provides a clean voxelized molecular representation. TIFF2026518674000026.tif3170 is a least squares estimator shown by equation (1) below. By applying TIFF2026518674000027.tif5170, the corresponding noisy voxelized molecular representation is obtained. It can be directly recovered from TIFF2026518674000028.tif4170. Least squares estimator TIFF2026518674000029.tif5170 is a noisy voxelized molecular representation. Noise present in TIFF2026518674000030.tif4170 By removing TIFF2026518674000031.tif3170, it acts as a noise remover, resulting in a clean voxelized molecular representation. Please understand that TIFF2026518674000032.tif3170 can be recovered.

number

[0119] As will be explained in more detail below, once the denoising model 117 is trained, the molecular design calculation model 115 applies the denoising model 117 to perform the “walk jump” generation process to determine the true data distribution. In TIFF2026518674000048.tif5170, output molecules exhibiting one or more desired properties of the molecules can be generated. For example, in some cases, the denoising model 117 may generate output molecules exhibiting noisy data distributions across multiple consecutive sampling iterations. You may also sample from TIFF2026518674000049.tif5170, each representing a noisy voxelized molecular representation. By at least denoising TIFF2026518674000050.tif4170, the noisy data distribution can be reduced. Includes a denoising model 117 that selects at least one sample from TIFF2026518674000051.tif5170. In some cases, noisy data distributions The sampling in TIFF2026518674000052.tif5170 shows a noisy data distribution where samples selected in one sample iteration are noisier than samples selected in another sample iteration. As originating from different locations in TIFF2026518674000053.tif5170, the score function This may be derived from TIFF2026518674000054.tif5170. Noisy data distribution This traverse of TIFF2026518674000055.tif5170 is the so-called "walking" part of the generation process.

[0120] In some cases, the data distribution is noisy. Instead of freely sampling from the entire TIFF2026518674000056.tif6170, use the score function TIFF2026518674000057.tif5170 is a condition Noisy data distribution based on TIFF2026518674000058.tif3170 (e.g., the gradient of the classifier) A molecule in a specific region within TIFF2026518674000059.tif7170 The sampling of TIFF2026518674000060.tif4170 may be limited. Therefore, in some cases, each consecutive sample may be a score function As indicated by the score output by TIFF2026518674000061.tif5170, the data distribution is noisy. A gradually increasing, more dense region may be selected from TIFF2026518674000062.tif5170. Here again, as mentioned, the score function Noisy data distribution induced by TIFF2026518674000063.tif5170 Traversing TIFF2026518674000064.tif5170 reveals a noisy data distribution. TIFF2026518674000065.tif5170 can be considered as "walking". Corresponding noisy voxelized molecular representation. Clean voxelized molecular representation from TIFF2026518674000066.tif4170 The recovery of TIFF2026518674000067.tif3170 is due to a noisy data distribution. True data distribution from TIFF2026518674000068.tif5170 This may constitute a "jump" to TIFF2026518674000069.tif5170. In some cases, this may be due to a noisy data distribution. True data distribution from TIFF2026518674000070.tif5170 The "jump" back to TIFF2026518674000071.tif5170 is a noisy voxelized molecular representation. Noise present in TIFF2026518674000072.tif4170 Remove TIFF2026518674000073.tif3170 and obtain the corresponding clean voxelized molecule representation. To recover TIFF2026518674000074.tif3170, this can be achieved by applying a denoising engine such as denoising engine 117. For example, in some cases, noisy voxelized molecular representations can be achieved. The least squares estimator is available in TIFF2026518674000075.tif4170. The denoising engine 117, which applies TIFF2026518674000076.tif5170, provides a clean voxelized molecular representation. TIFF2026518674000077.tif3170 can be recovered.

[0121] In some exemplary embodiments, the training engine 120 may generate each corrupted sample molecule in the training dataset by adding noise to the embedding of the noisy three-dimensional representation of the sample molecule. For example, Figure 1B shows that, in some cases, the corruption engine 121 may generate a corrupted embedding 188 by adding at least noise (e.g., Gaussian noise such as isotropic Gaussian noise) to the embedding 186 of the noisy three-dimensional representation 182 of the sample molecule (e.g., a noisy voxelized representation) (not directly to the noisy three-dimensional representation 182 of the sample molecule). Figure 1B further shows that the embedding 186 may be generated by an encoder 111 that downsamples (or compresses) the noisy three-dimensional representation 182 of the sample molecule. Downsampling (or compressing) the noisy three-dimensional representation 182 of the sample molecule may reduce the dimensionality of the noisy three-dimensional representation 182 of the sample molecule. For example, if the noisy three-dimensional representation 182 of a sample molecule is a [32×32×32] voxel grid containing 32,000 features (or atomic density values), downsampling (or compression) may produce a [4×4×4] voxel grid containing 64 features (or atomic density values). Thus, downsampling (or compression) of the noisy three-dimensional representation 182 of a sample molecule can increase the overall speed and efficiency of the generation process. In some cases, it may be possible to generate a large number of candidate molecules, e.g., tens of thousands or even millions of candidate molecules, in a short period of time to support low-yield applications such as computational drug design where most candidate molecules cannot be successfully synthesized in the laboratory. Downsampling (or compression) of the three-dimensional representation 182 of a sample molecule can also enable the generation of larger molecules (e.g., molecules containing more than 200 atoms), which can be very cumbersome to operate if they are retained in their original three-dimensional representation without downsampling (or compression).

[0122] In step 204, the molecular design engine 110 may train the molecular design computation model 115 by applying it to recover the three-dimensional representation of each corrupted sample molecule in the training dataset from the corrupted three-dimensional representation of the sample molecule. In some exemplary embodiments, step 204 of training the molecular design computation model 115 may include training a denoising model 117, based on at least the training dataset, to approximate a noisy data distribution (or noisy latent distribution) of molecules exhibiting one or more desired properties. For example, in the example shown in Figure 1A, the denoising model 117 may be trained to recover a noisy three-dimensional representation 184 (e.g., a voxelized representation) of the sample molecule from a corrupted three-dimensional representation 182 of the sample molecule. In the example shown in Figure 1B, the denoising model 117 may be trained to recover an embedding 186 of the noisy three-dimensional representation 182 of the sample molecule from a corrupted embedding 188. In each example, it should be understood that the denoising engine 117 may be trained on a noisy three-dimensional representation 182 of the sample molecule rather than a clean three-dimensional representation of the sample molecule, in order for the denoising engine 117 to approximate a noisy data distribution that exhibits smoother density transitions than the true data distribution.

[0123] In the example shown in Figure 1A, training the molecular design calculation model 115 may include adjusting one or more parameters (e.g., weights, biases, etc.) of the denoising model 117 to reduce (or minimize) the difference (e.g., mean squared error (MSE)) between the noisy three-dimensional representation 182 of the sample molecule recovered by the denoising model 117 and the original noisy three-dimensional representation 182 of the sample molecule. Furthermore, training the denoising model 117 may include determining a function 175 that is parameterized by the parameters (e.g., weights, biases, etc.) of the denoising model 117. For example, in some cases, the function 175 may be a scoring function that outputs a value (e.g., a score) that indicates a local change in the density (or gradient) of the data distribution. Therefore, in some cases, function 175 may output a first value (e.g., a first score) indicating a first local change in the density of the data distribution at a first location occupied by a first numerator, and a second value (e.g., a second score) indicating a second local change in the density of the data distribution at a second location occupied by a second numerator. For example, the score function may assign a first score to a first sample that shows a more positive local change (e.g., an increase or a smaller decrease) in the density of the first data distribution at the first location of the first sample, and a second score to a second sample that shows a less positive local change (e.g., a smaller increase or decrease) in the density of the first data distribution at the second location of the second sample. If function 175 is a score function, sampling of the data distribution may be induced by the value (e.g., score) output by function 175. As described in more detail below, sampling of the data distribution may be guided by function 175 such that the sample (or molecule) is selected from an increasingly dense region of the data distribution, which is likely to be occupied by one or more molecules exhibiting a desired property.

[0124] In the example shown in Figure 1B, training the denoising model 117 may involve tuning one or more parameters of the denoising model 117 (e.g., weights, biases, etc.) to reduce (or minimize) the difference (e.g., mean squared error (MSE)) between the original undamaged embedding 188 and the embedding 186 of the noisy three-dimensional representation 182 of the sample molecules recovered from the embeddedding 186 damaged by the denoising model 117. In doing so, the parameters of the function 175 can also be tuned. Similarly, if the function 175 is a score function, the parameters of the function 175 may be tuned so that the function 175 outputs a higher value (e.g., a higher score) for a first molecule occupying a first location in the data distribution that shows a more positive local change in the density of the data distribution (e.g., a positive gradient showing a transition from a low-density region to a high-density region of the data distribution) than for a second molecule occupying a second location in the data distribution that shows a more positive local change in the density of the data distribution.

[0125] In some exemplary embodiments, the molecular design engine 110 may train a molecular design computation model 115, including a denoising model 117, by approximating the function 175 by performing at least gradient-based Markov chain Monte Carlo (MCMC) sampling, such as Markov chain Monte Carlo (MCMC) sampling using Langevin dynamics. In some cases, the function 175 may output a value (e.g., a score) that indicates transitions between different density regions of the data distribution. For example, as a score function, the value (e.g., score) output by the function 175 for each molecule may indicate a local change in density (or gradient) at the corresponding location in the data distribution. In the example shown in Figure 1A, gradient-based Markov chain Monte Carlo (MCMC) sampling to determine function 175 may include adjusting the parameters of denoising model 117 (e.g., weights, biases, etc.) and the parameters of function 175 over multiple iterations to increase (or maximize) the similarity between the noisy three-dimensional representation 182 of the sample molecule recovered by denoising model 117 and the original three-dimensional representation 182 of the sample molecule (e.g., by reducing (or minimizing) the mean squared error (MSE)). In the example shown in Figure 1B, one or more parameters of denoising model 117 and the parameters of function 175 may be adjusted over multiple iterations of gradient-based Markov chain Monte Carlo (MCMC) to increase (or maximize) the similarity between the embedding 186 of the noisy three-dimensional representation 182 of the sample molecule recovered from the corrupted embedding 188 by denoising engine 117 and the original uncorrupted embedding 186 (e.g., by reducing (or minimizing) the mean squared error (MSE)).

[0126] As mentioned above, the denoising model 117 can be trained to recover a noisy three-dimensional representation 182 (e.g., a noisy voxelized representation) of the sample molecule in order to avoid overfitting the denoising model 117 to known molecules available for training. When a relatively small number of known molecules characterizing the high-dimensional data distribution are available, directly training the denoising model 117 based on the known molecules may produce an overly jagged energy landscape with abrupt gradient changes between regions occupied by the known molecules. Sampling from the data distribution while being led by steep gradients may not adequately explore the data distribution, as sampling may be limited to regions very close to the known molecules, at least due to the steepness of the gradients. In contrast, training the denoising model 117 based on a noisy three-dimensional representation 182 (e.g., a noisy voxelized representation) of the sample molecule results in smoother density transitions, gentler gradients in function 175, and more efficient exploration of the data distribution when sampling from there.

[0127] In 206, the molecular design engine 110 may generate an output molecule by applying a trained molecular design computation model 115, at least by denoising the voxelized representation of the input molecule. In some exemplary embodiments, the molecular design computation model 115 may generate an output molecule 162 by using a denoising model 117 to update at least the three-dimensional representation (e.g., voxelized representation) of the input molecule 152, or optionally its embedding 154, while being induced by a function 175. For example, the molecular design computation model 115 in Figure 1A may directly update the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 without downsampling or compression. Alternatively, the molecular design computation model 115 in Figure 1B may update the embedding 154 of the three-dimensional representation of the input molecule 152, which may be generated by an encoder 111 that downsamples (or compresses) the three-dimensional representation (e.g., voxelized representation) of the input molecule 152. By doing so, the dimensionality (or number of features) of the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 can be reduced so that the resulting embedding 154 can be more compact than the original (or uncompressed) three-dimensional representation of the input molecule 152. For example, the original three-dimensional representation (e.g., voxelized representation) of the input molecule 152 may contain a [32×32×32] voxel grid with 32,000 features (or atomic density values), while the embedding 154 may contain a [4×4×4] voxel grid with 64 features (or atomic density values). It should be understood that the encoder 111 can be trained to downsample (or compress) the voxelized representation of the input molecule 152 so that the resulting embedding 154 conveys the same (or similar) information as the voxelized representation of the input molecule 152 in its original (or uncompressed) form. In some cases, the encoder 111 may be part of an autoencoder (e.g., a variational autoencoder (VAE) such as a vector quantization variational autoencoder (VQ-VAE)) which also includes a decoder 119. In some cases, the encoder 111 may be trained to generate embeddings 154 so that the decoder 119 can recover the original voxelized representation of the input molecule 152 by decoding at least the embeddings 154.

[0128] In some cases, the molecular design calculation model 115 can denoise the input molecule 152 by at least updating the three-dimensional representation of the input molecule 152, or by updating the embedding 154 of the three-dimensional representation of the input molecule 152. As mentioned above, in some cases, the three-dimensional representation of the input molecule 152 may be a voxelized representation of the input molecule 152, where the types and positions of atoms present in the input molecule 152 are represented as a continuous (e.g., Gaussian) atomic density centered on the atoms. For example, in some cases, the voxelized representation of the input molecule 152 may be n 3 The voxelized representation of the input molecule 152 may include an n×n×n voxel grid containing a quantity of voxels, each associated with a value indicating the atomic density at its corresponding location. In some cases, the atomic density associated with a single voxel may have a range of values, such as [0,1], where the lower limit of the range indicates that the voxel is far from any atom in the input molecule 152, and the upper limit of the range indicates that the voxel is close to the center of the atoms in the input molecule 152. Furthermore, in some cases, the voxelized representation of the input molecule 152 may include multiple channels, each corresponding to a different type of atom that may be present in the input molecule 152. Thus, in some cases, the voxelized representation of the input molecule 152 may represent the types and locations of atoms present in the input molecule 152 as a continuous (e.g., Gaussian) atomic density across one or more channels.

[0129] In some exemplary embodiments, denoising of the input molecule 152 may include updating the three-dimensional representation of the input molecule 152, or alternatively, updating the embedding 154 of the input molecule 152. If the molecular design calculation model 115 operates on the three-dimensional representation of the input molecule 152, or if the embedding 154 is generated without downsampling (or compression) of the three-dimensional representation of the input molecule 152, denoising may include updating the atomic density of one or more voxels in at least one channel of the noisy voxelized representation of the input molecule 152. Doing so may be equivalent to adding, removing, and / or rearranging one or more atoms of different atomic types in the input molecule 152. For example, increasing (or decreasing) the atomic density of one or more voxels in one channel of the noisy voxelized representation of the input molecule 152 may be equivalent to adding (or removing) atoms of the corresponding type to the input molecule 152. Alternatively and / or additionally, decreasing the atomic density of the first voxel while increasing the atomic density of the second voxel may be equivalent to rearranging atoms from the first location in the first voxel to the second location in the second voxel.

[0130] Alternatively, if the molecular design calculation model 115 operates on an embedding 154 of a three-dimensional representation (e.g., a voxelized representation) of the input molecule 152, denoising may include updating the values ​​of the voxels present in the embedding 154. As previously mentioned, the embedding 154 can be generated by an encoder 111 that condenses at least some of the features (e.g., atomic density values) present in the voxelized representation of the input molecule 152. The embedding 154 may contain fewer features than the original voxelized representation of the input molecule 152, but can still convey the same (or similar) information as the original three-dimensional representation of the input molecule 152. Therefore, denoising the embedding 154 may include updating one or more values ​​present in the embedding 154, at least some of which may represent multiple features (or atomic density values) from the original voxelized representation of the input molecule 152.

[0131] Updating the three-dimensional representation of the input molecule 152 or its embedding 154 in the manner described above may involve selecting a sample (or updated molecule) from a noisy data distribution (or noisy latent distribution) of molecules exhibiting one or more desired characteristics. In the case of gradient-based Markov chain Monte Carlo (MCMC) sampling, the update may be guided by the output of function 175 (e.g., the score output by function 175) such that the sample (or updated molecule) selected during each successive sampling iteration originates from an increasingly dense region of the noisy data distribution, where it is more likely that the sample (or updated molecule) is occupied by one or more molecules exhibiting one or more desired characteristics.

[0132] To elaborate further, in some cases, the three-dimensional representation of the input molecule 152 or its embedding 154 may undergo a first update and a second update. Doing so may be equivalent to selecting a first sample (or first updated molecule) and a second sample (or second updated molecule) from a noisy data distribution. In some cases, after selecting a first sample (or first updated molecule) and a second sample (or second updated molecule) from a noisy data distribution (or noisy latent distribution), the molecular design calculation model 115 may apply function 175 to determine a value (e.g., a score and / or similar) that indicates the likelihood of each sample (or updated molecule) in the noisy data distribution (or noisy latent distribution). If function 175 is a score function, for example, a higher value (e.g., a lower score) may indicate that the sample (or updated molecule) is selected from a region of the noisy data distribution that exhibits a larger positive local change in density (e.g., an increase or a smaller decrease), or similarly, that the sample (or updated molecule) is more likely to be located within the noisy data distribution. Thus, in some cases, after selecting the first sample (or first updated molecule) and the second sample (or second updated molecule), the molecular design calculation model 115 may apply the denoising model 117 to continue updating the three-dimensional representation of the input molecule 152 or its embedding 154 to select additional samples (or further updated molecules) from increasingly dense regions of the noisy data distribution until, for example, a sample (or updated molecule) exhibiting a threshold likelihood located within the noisy data distribution (or latent distribution) is selected. For example, in some cases, the denoising model 117 may be applied to further modify the three-dimensional representation of the input molecule 152 or embedding 154 having the first update (or first update molecule) instead of the second update (or second update molecule), if the three-dimensional representation of the input molecule 152 or embedding 154 having the first update (or first update molecule) is selected from a denser region of the data distribution. Doing so may be analogous to traversing a noisy data distribution (or noisy latent distribution) and sampling from a gradually increasing density region of the noisy data distribution.If the denoising model 117 modifies the embedding 154 of the three-dimensional representation of the input molecule 152, the denoising model 117 may operate in a noisy latent space that may reflect similarities (or differences) in the types and positions of atoms within the molecule where the distance between two or more embeddings differs. Abrupt transitions in density where the true data distribution of molecules exhibiting one or more desired properties exists can be smoothed by adding noise. Since the denoising model 117 is trained to approximate the data distribution of molecules exhibiting a particular desired property (e.g., drug-like properties), the updates made to the embedding 154 when denoising the input molecule 152 may coincide with the types and positions of atoms found in molecules exhibiting one or more desired properties. Therefore, the same desired properties may also exist in the output molecule 162 generated by the molecular design calculation model 115, which denoises the input molecule 152 by applying the denoising model 117.

[0133] Figure 3A shows a flowchart illustrating an example of a process 300 for training a molecular design computation model 115 according to several exemplary embodiments. Referring to Figures 1-2 and 3A, process 300 may perform operation 204 of process 200 shown in Figure 2. In some cases, process 300 may be performed by the molecular design engine 110 to train the molecular design computation model 115, including, for example, a denoising model 117, to approximate the noisy data distribution of a noisy three-dimensional representation (e.g., a noisy voxelized representation) of a molecule exhibiting one or more desired properties. In some cases, as will be described in more detail below, the molecular design computation model 115, including the denoising model 117, may be trained to approximate a noisy data distribution instead of the true data distribution in order to avoid overfitting the molecular design computation model 115 to known molecules available for training the molecular design computation model 115. Furthermore, in some cases, the molecular design calculation model 115, including the denoising model 117, may be trained through gradient-based Markov chain Monte Carlo (MCMC) sampling, such as Markov chain Monte Carlo (MCMC) sampling using Langevin dynamics.

[0134] In step 302, the molecular design engine 110 may apply a molecular design computation model having a first adjustment for denoising the corrupted sample molecules and generating a first updated molecule. In some exemplary embodiments, step 302 may include the molecular design engine 110 approximating a data distribution of three-dimensional representations (e.g., voxelized representations) of one or more molecules exhibiting the same desired properties, by training a molecular design computation model 115, including, for example, a denoising model 117, so that candidate molecules exhibiting the same desired properties can be generated from there. In some cases, the molecular design computation model 115 may be trained to approximate the aforementioned data distribution based on a training dataset of corrupted sample molecules, each of which is generated based on a noisy three-dimensional representation (e.g., voxelized representation) of the sample molecule (e.g., a known molecule) from the data distribution. An example of this is shown in Figure 1A, where the molecular design computation model 115 (e.g., denoising model 117) is trained to recover a noisy three-dimensional representation 182 of the sample molecule from a corrupted three-dimensional representation 184 of the sample molecule generated by the corruption engine 121. In some cases, instead of being trained to directly recover noisy three-dimensional representations (e.g., voxelized representations) of sample molecules, the molecular design calculation model 115 may be trained based on corrupted embeddings of those three-dimensional representations (e.g., voxelized representations). This is shown in Figure 1B, where the molecular design calculation model 115 (e.g., denoising model 117) is trained to recover the embedding 186 of the noisy three-dimensional representation 182 of the sample molecule from the corrupted embedding 188 generated by the corruption engine 121.

[0135] In some exemplary embodiments, training the molecular design computation model 115 may include applying a denoising model 117 to denoise a corrupted three-dimensional representation (e.g., a voxelized representation) or its corrupted embedding for each sample molecule. Figure 1A shows an example in which training the molecular design computation model 115 includes adjusting the parameters of the denoising model 117 (e.g., weights, biases, etc.) to gradually reduce the difference (e.g., mean squared error (MSE)) between the noisy three-dimensional representation (e.g., a voxelized representation) of the sample molecule and the corrupted three-dimensional representation of the sample molecule recovered by the denoising model 117, for example, over multiple iterations. Alternatively, in the example shown in Figure 1B, the molecular design computation model 115 may be trained by adjusting the parameters of the denoising model 117 (e.g., weights, biases, etc.) to gradually reduce the difference (e.g., mean squared error) between the embedding of the noisy three-dimensional representation of the sample molecule and the embedding recovered by the denoising model 117 from the corresponding corrupted embedding, over multiple iterations. In some cases, the parameters of the denoising model 117 (e.g., weights, biases, etc.) may undergo different adjustments before further adjustments are made for adjustments that result in a lower difference (e.g., mean squared error (MSE)). For example, in some cases, the first adjustment may be made to the parameters of the denoising model 117 (e.g., weights, biases, etc.) before the denoising model 117 having the first adjustment is applied to denoise a corrupted three-dimensional representation of the sample molecule or a corrupted embedding of the three-dimensional representation of the sample molecule and generate at least a first updated molecule. In some cases, the first updated molecule may be an updated three-dimensional representation of the first molecule (e.g., a voxelized representation), or an updated embedding of the three-dimensional representation of the first molecule (e.g., a voxelized representation).

[0136] In some cases, a corrupted three-dimensional representation or corrupted embedding of a sample molecule's three-dimensional representation can be denoised by updating one or more atomic density values ​​that represent the types and locations of atoms present in the sample molecule. If the corrupted embedding is generated by downsampling (or compressing) the three-dimensional representation of the sample molecule, at least some of the updated values ​​may condense several features (or atomic density values) from the original three-dimensional representation of the sample molecule (e.g., a voxelized representation). As will be described in more detail below, a denoising model 117 having a second adjustment (instead of the first adjustment) can be applied to denoise the corrupted three-dimensional representation of the sample molecule (e.g., a corrupted voxelized representation) or the corrupted embedding of the three-dimensional representation of the sample molecule, generating at least a second updated molecule. Further adjustments may be made to the denoising model 117 having either the first or second adjustment. By doing so, the denoising model 117 may be trained to approximate a noisy data distribution, or in some cases a noisy latent distribution, which exhibits smoother density transitions to support more efficient sampling because there are no steep gradient changes that restrict sampling to the immediate vicinity of the sample molecules that form the basis of the training dataset.

[0137] In some exemplary embodiments, training the denoising model 117 may further include determining the function 175. As previously mentioned, in some cases the function 175 may be a score function parameterized by the parameters of the denoising model 117 (e.g., weights, biases, etc.). Thus, in some cases training the molecular design computation model 115, which involves tuning the parameters of the denoising model 117, may also include tuning the parameters of the function 175. For example, in some cases the function 175 may be determined by performing gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling) to approximate the gradient of a noisy data distribution (or noisy latent distribution). Doing so may involve tuning the parameters of the function 175 over one or more iterations so that the function 175 outputs a value (e.g., a score) that indicates a local density change in the noisy data distribution (or noisy latent distribution). If function 175 is a score function, the parameters of function 175 may be adjusted so that function 175 assigns higher values ​​(e.g., higher scores) to samples from locations exhibiting more positive local changes in density (e.g., decreases or smaller decreases) than from locations exhibiting more positive local changes in density (e.g., increases or smaller decreases). Thus, once the denoising model 117 is trained, function 175 may output values ​​(e.g., scores and / or similar) that distinguish between samples from high-density regions of a noisy data distribution (or noisy latent distribution) (e.g., three-dimensional representations, embeddings of three-dimensional representations, etc.) and samples sampled from low-density regions of the noisy data distribution.

[0138] In step 304, the molecular design engine 110 may apply a molecular design calculation model having a second adjustment to denoise the damaged sample molecule and generate a second updated molecule. In some exemplary embodiments of step 304, if a denoising model 117 having a first adjustment is applied to generate at least a first updated molecule, a denoising model 117 having a second adjustment may be applied to generate at least a second updated molecule, such as an updated three-dimensional representation (e.g., an updated voxelized representation of the second molecule or an updated embedding of the three-dimensional representation of the second molecule). It should be understood that the first and second adjustments may involve different changes to the parameters of the denoising model 117 (e.g., weights, biases, etc.). Therefore, applying a denoising model 117 with a second adjustment to denoise a corrupted three-dimensional representation 184 of a sample molecule or a corrupted embedding 186 of a noisy three-dimensional representation 182 of a sample molecule may result in a different updated molecule than applying a denoising model 117 with a first adjustment to denoise a corrupted three-dimensional representation 182 of a sample molecule or a corrupted embedding 186 of a noisy three-dimensional representation 182 of the same sample molecule. As will be described in more detail below, training the denoising model 117 may also involve further adjusting the denoising model 117 with either the first or second adjustment in accordance with the difference (e.g., mean squared error (MSE)) present in the noisy three-dimensional representation 182 of a sample molecule (Figure 1A) or the embedding 184 of a noisy three-dimensional representation 182 of a sample molecule (Figure 1B) recovered by the denoising model 117.

[0139] In step 306, the molecular design engine 110 may determine that the first updated molecule is more similar to the sample molecule than the second updated molecule. In some exemplary embodiments, step 306 may also include the molecular design engine 110 selecting the denoising model 117 with the first adjustment instead of the denoising model 117 with the second adjustment if the first updated molecule generated by the denoising model 117 with the first adjustment is more similar (e.g., exhibits a lower mean squared error (MSE)) to the noisy three-dimensional representation of the sample molecule (or its embedding) than the second updated molecule generated by the denoising model 117 with the second adjustment. For example, in Figure 1A, the first updated molecule may be an updated three-dimensional representation of the first molecule that has a smaller difference (e.g., a lower mean squared error (MSE)) compared to the noisy three-dimensional representation 182 of the sample molecule than the second updated molecule. In Figure 1B, the first updated molecule may be an updated embedding of the three-dimensional representation of the first molecule that has a smaller difference (e.g., a lower mean squared error (MSE)) than the second updated molecule in the embedding 186 of the noisier three-dimensional representation 182 of the sample molecule.

[0140] The fact that the first updated molecule is more similar to the noisy three-dimensional representation 182 of the sample molecule (or its embedding 186) than the second updated molecule may indicate that the denoising model 117 with the first adjustment is better at recovering the noisy three-dimensional representation 182 of the sample molecule (or its embedding 186) than the denoising model 117 with the second adjustment. Therefore, the denoising model 117 with the first adjustment may better approximate the noisy data distribution (or noisy latent distribution) of molecules exhibiting one or more desired properties than the denoising model 117 with the second adjustment. Thus, in some cases, the molecular design engine 110 may select the denoising model 117 with the first adjustment instead of the denoising model 117 with the second adjustment to undergo one or more additional iterations of adjustment.

[0141] In 308, the molecular design engine 110 may further adjust the molecular design calculation model having the first adjustment instead of the second adjustment until one or more criteria are met. In some exemplary embodiments, the molecular design engine 110 may further adjust the denoising model 117 having the first adjustment if the first updated molecule generated by the denoising model 117 having the first adjustment is more similar (e.g., has a lower mean squared error (MSE)) to the noisy three-dimensional representation 182 of the sample molecule (or its embedding 186) than the second updated molecule generated by the denoising model 117 having the second adjustment. For example, during subsequent iterations of adjustment, the molecular design engine 110 may further adjust the parameters (e.g., weights, biases, etc.) of the denoising model 117 having the first adjustment before applying the further adjusted denoising model 117 to generate one or more additional updated molecules. In some cases, the denoising model 117 may be further adjusted to further increase the similarity (or decrease the mean squared error (MSE)) between the updated molecules generated by the denoising model 117 and the noisy three-dimensional representations (or their embeddings) of sample molecules in the training dataset. In some cases, the molecular design engine 110 may continue to adjust the denoising model 117 until one or more criteria are met. For example, in some cases, the molecular design engine 110 may continue to adjust the parameters of the denoising model 117 (e.g., weights, biases, etc.) until the molecular design engine 110 performs iterations of the threshold amount of adjustment. Alternatively and / or additionally, the molecular design engine 110 may continue to adjust the parameters of the denoising model 117 (e.g., weights, biases, etc.) until the similarity (e.g., mean squared error (MSE)) between the updated molecules generated by the denoising model 117 and the noisy three-dimensional representations (or their embeddings) of sample molecules in the training dataset meets one or more thresholds.In some cases, the molecular design engine 110 may continue to adjust the parameters of the denoising model 117 (e.g., weights, biases, etc.) until the updated molecules generated by the denoising model 117 exhibit a threshold likelihood in the data distribution of molecules representing one or more desired characteristic training datasets.

[0142] As will be explained in more detail below, if one or more criteria are met, the trained denoising model 117 can be applied to generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162 by at least denoising the three-dimensional representation (e.g., a voxelized representation) of the input molecule 152. As shown in Figures 1A and 1B, the trained denoising model 117 can generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162 by at least sampling from a noisy data distribution occupied by noisy three-dimensional representations (e.g., voxelized representations) of molecules exhibiting one or more desired properties (e.g., drug-like properties), or from a noisy latent distribution occupied by embeddings of noisy three-dimensional representations (e.g., voxelized representations) of molecules, based on the function 175. Sampling may include one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo), which can be derived by function 175 such that each sampling iteration involves selecting one or more samples (or molecules) from an incrementally dense region of a noisy data distribution (or noisy latent distribution).

[0143] Figure 3B is a flowchart illustrating an example of process 325 for applying a molecular design computation model to generate a three-dimensional molecule in voxelized space, according to several exemplary embodiments. Referring to Figures 1A, 1B, 2, and 3B, process 325 may perform operation 206 of process 200 shown in Figure 2. In some cases, process 325 may be performed by a molecular design engine 110. For example, in some cases, the molecular design engine 110 may generate a three-dimensional representation (e.g., a voxelized representation) of an output molecule by applying a molecular design computation model 115 (e.g., a denoising model 117) to at least denoising the three-dimensional representation (e.g., a voxelized representation) of an input molecule. In some cases, the input molecule may be a random molecule (e.g., a molecule with a random selection of atomic types and / or positions) or a known molecule having one or more desired properties. Therefore, the three-dimensional representation of the input molecule (e.g., a voxelized representation) may contain noise that needs to be removed by the molecular design calculation model 115 so that the resulting three-dimensional representation of the output molecule (e.g., a voxelized representation) matches a molecule exhibiting one or more desired properties (e.g., drug-like properties). The molecular design calculation model 115 can denoise the three-dimensional representation of the input molecule (e.g., a voxelized representation) by sampling at least from a noisier data distribution (or a noisier latent distribution) that is more efficient to sample. This is because the smoother density transitions present within it allow for a better exploration of the data distribution. As will be described in more detail below, once the molecular design calculation model 115 generates a three-dimensional representation of the output molecule (e.g., a voxelized representation), the molecular design engine 110 may further generate one or more other representations of that output molecule, including, for example, a one-dimensional representation of the output molecule, a two-dimensional representation of the output molecule, and so on. The fact that an output molecule is generated by manipulating the three-dimensional representation (e.g., voxelized representation) of an input molecule, which captures the conformation (or three-dimensional structure) of the input molecule, means that the conformation (or three-dimensional) structure of the output molecule is more likely to match one or more desired properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development).

[0144] In 332, the molecular design engine 110 may update the three-dimensional representation of the input molecule to generate an updated three-dimensional representation. In some exemplary embodiments, updating the three-dimensional representation may include the molecular design engine 110 applying a molecular design calculation model 115 to generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162 by at least denoising the three-dimensional representation (e.g., a voxelized representation) of the input molecule 152. An example of this process is shown in Figure 1A, where the denoising engine 117 denoises the three-dimensional representation of the input molecule 152 to generate an updated three-dimensional representation 160. In some cases, the input molecule 152 may be a noise molecule (e.g., a molecule with randomly selected atomic types and / or positions) or a known molecule having one or more undesirable properties. This means that the three-dimensional representation of the input molecule 152 may contain at least some noise that would cause it to contradict that of a molecule exhibiting one or more desired properties (e.g., drug-like properties). Therefore, in some cases, the denoising engine 117 may be trained to update the three-dimensional representation of the input molecule 152 so that the resulting updated three-dimensional representation 160 matches the three-dimensional representation of a molecule exhibiting one or more desired properties.

[0145] In some exemplary embodiments, the molecular design calculation model 115 may apply a denoising model 117 to update the three-dimensional representation of the input molecule 152 based on a function 175. In some cases, function 175 may be a scoring function that outputs a value (e.g., a score and / or similar) indicating the likelihood that each sample (or molecule) selected from a noisy data distribution is in a noisy data distribution. For example, in some cases, the value output by function 175 for a particular sample (or molecule) may indicate a local change in density where the sample (or molecule) is selected. The denoising model 117 may update the three-dimensional representation of the input molecule 152 over a series of consecutive sampling iterations, based at least on the values ​​output by function 175. During each sampling iteration, the denoising model 117 may be applied to further update the three-dimensional representation of the input molecule 152 so that the resulting updated three-dimensional representation 160 is selected from a denser region of the noisier data distribution than those selected in one or more previous sampling iterations.

[0146] In some exemplary embodiments, the molecular design calculation model 115 may perform gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling) of a noisy data distribution, in which the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 is updated over a series of consecutive sampling iterations. In some cases, each iteration may include the molecular design calculation model 115 further updating the three-dimensional representation of the input molecule 152 to sample from increasingly dense regions of the noisy data distribution. Furthermore, in some cases, the updates made to the three-dimensional representation of the input molecule 152 may be accumulated over a series of consecutive iterations. For example, in some cases, the three-dimensional representation of the input molecule 152 may undergo a first update and a second update. The molecular design calculation model 115 may apply function 175 to determine a first value (e.g., a first score) for the three-dimensional representation of the input molecule 152 with a first update and a second value (e.g., a second score) for the three-dimensional representation of the input molecule 152 with a second update. During subsequent iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling, the denoising model 117 may be applied to further update the three-dimensional representation of the input molecule 152 with a first update if the first and second values ​​indicate that the three-dimensional representation of the input molecule 152 with a first update is sampled from a denser region of the noisy data distribution and exhibits a higher likelihood of being in a noisier data distribution than the three-dimensional representation of the input molecule 152 with a second update.

[0147] In some cases, one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling may be performed, in which case the molecular design calculation model 115 applies a denoising model 117 to further modify the three-dimensional representation of the input molecule 152 until one or more criteria are met. For example, in some cases, the molecular design calculation model 115 may perform one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling until a threshold quantity sampling iteration is performed. Alternatively and / or additionally, the molecular design calculation model 115 may perform one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling until the function 175 outputs a value (e.g., a score and / or similar) that satisfies one or more thresholds for the updated three-dimensional representation 160. The fact that the updated three-dimensional representation 160 and the associated values ​​(e.g., scores and / or similar) satisfy one or more thresholds may indicate that the updated three-dimensional representation 160 was selected from a region of a noisy data distribution with a sufficiently high density, and that the likelihood of the updated three-dimensional representation 160 being within a noisy data distribution satisfies one or more thresholds. In some cases, one or more criteria may also include generating an output molecule of a threshold quantity exhibiting one or more desired properties (e.g., at least one output molecule exhibiting a threshold level for one or more drug-like properties such as affinity, specificity, biological activity, or developability).

[0148] In step 336, the molecular design engine 110 may denoise the updated three-dimensional representation to generate a three-dimensional representation of the output molecule. In some exemplary embodiments of step 336, the molecular design calculation model 115 may denoise the three-dimensional representation of the input molecule 152 by sampling from a noisy data distribution occupied by noisy three-dimensional representations of molecules exhibiting one or more desired properties. As previously stated, the molecular design calculation model 115, including the denoising model 117, may be trained to approximate a noisy data distribution (instead of the true data distribution) by at least being trained to denoise a corrupted three-dimensional representation 182 of the sample molecule in order to recover a noisy three-dimensional representation 184 of the sample molecule, rather than a clean three-dimensional representation of the sample molecule. Furthermore, this noisy data distribution may exhibit smoother density transitions and is therefore more efficient to sample. The fact that the updated three-dimensional representation 160 is sampled from a noisy data distribution means that the updated three-dimensional representation 160 may undergo additional denoising. For example, Figure 1A shows that the molecular design engine 110 may apply a recovery model 118 to denoise the updated three-dimensional representation 160 and generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162 from it. In some cases, the recovery model 118 may be trained to denoise the updated three-dimensional representation 160 in order to remap the updated three-dimensional representation 160 from a noisy data distribution to a true data distribution of molecules exhibiting one or more desired properties (e.g., drug-like properties). It should be understood that this denoising differs from the denoising of the denoising model 117 trained to perform, and involves updating the three-dimensional representation of the input molecule 152 to sample from a high-density region of a noisy data distribution that is likely to be occupied by molecules exhibiting one or more desired properties.

[0149] In 338, the molecular design engine 110 may generate one or more other representations of the output molecule based on at least the three-dimensional representation of the output molecule. In some exemplary embodiments, the three-dimensional representation of the output molecule 162 (e.g., a voxelized representation) generated by the recovery model 118, which denoises the updated three-dimensional representation 160 sampled from a noisy data distribution by the molecular computation model 115, may be further transformed into one or more other representations of the output molecule 162. For example, in some cases, the molecular design engine 110 may recover the positions (e.g., coordinates) of atoms present in the output molecule 162 and one or more bonds between them, based on at least the three-dimensional representation (e.g., a voxelized representation) of the output molecule 162. In doing so, the molecular design engine 110 may determine other representations of the output molecule 162, including, for example, a one-dimensional representation of the output molecule 162 (e.g., a Simplified Molecular Input Line Input System (SMILES) string), a two-dimensional representation of the output molecule 162 (e.g., a molecular graph), and the like. In some cases, the molecular design engine 110 may recover the positions of atoms present in the output molecule 162 by applying a peak detection technique that determines the positions (e.g., coordinates) of atoms based on one or more peaks in the atomic density contained in the three-dimensional representation (e.g., voxelized representation) of the output molecule 162, before determining one or more interconnection bonds based on the positions of atoms. Alternatively, the molecular design engine 110 may apply a machine learning model trained to convert the voxelized representation of the output molecule 162 into one or more other representations.

[0150] Figure 3C shows a flowchart illustrating an example of a process 350 for applying a molecular design computation model to generate a three-dimensional molecule in voxelized space, according to several exemplary embodiments. Referring to Figures 1-2 and 3C, process 350 may perform operation 206 of process 200 shown in Figure 2. In some cases, process 350 may be performed by a molecular design engine 110. For example, in some cases, the molecular design engine 110 may apply a molecular design computation model 115 (e.g., denoising model 117) to generate a three-dimensional representation of an output molecule, such as a voxelized representation of an output molecule, by at least denoising the three-dimensional representation of the input molecule (e.g., a voxelized representation). In some cases, the three-dimensional representation of the input molecule may be denoised by at least updating the embedding of the three-dimensional representation of the input molecule (e.g., a voxelized representation), and the three-dimensional representation of the input molecule may not be directly updated, at least because the embedding may be more compact and the computational efficiency of the operation may be higher. In some cases, the embedding of the three-dimensional representation of the input molecule can be generated by downsampling (or compressing) the three-dimensional representation of the input molecule, but it is also possible to generate the embedding without downsampling (or compressing) the three-dimensional representation of the input molecule. In the former case, the embedding of the three-dimensional representation of the input molecule may occupy a latent voxelization space, while in the latter case, the embedding of the three-dimensional representation of the input molecule may remain in the same discrete voxelization space as the original three-dimensional representation of the input molecule. It should be understood that the latent voxelization space may have a lower dimension than the discrete voxelization space so that operating on the embedding of the three-dimensional representation of the input molecule can increase the speed and computational efficiency of the generation process while achieving equivalent or better generation performance.

[0151] It should be understood that the molecular design calculation model 115 can denoise the embedding of the three-dimensional representation of the input molecule by sampling from a noisy latent distribution. That is, as mentioned above, the molecular design calculation model 115 can be trained to approximate a noisy latent distribution rather than the true data distribution, thereby avoiding at least the steep density transitions present in the true data distribution. In other words, the updated embedding generated by the molecular design calculation model 115, which updates the embedding of the three-dimensional representation of the input molecule, may still occupy a noisy latent distribution. This noisy latent distribution may be more efficient to sample because its smoother density transitions support a proper search of the data distribution. As will be explained in more detail below, the updated embedding may undergo decoding and further denoising to "jump" back to the true data distribution. Furthermore, in some cases, the molecular design engine 110 may generate one or more other representations of the output molecule, including, for example, a one-dimensional representation of the output molecule, a two-dimensional representation of the output molecule, etc., based on the three-dimensional representation of the output molecule resulting from the decoding and denoising of the updated embedding. The fact that an output molecule is generated by manipulating the three-dimensional representation (e.g., voxelized representation) of an input molecule, which captures the conformation (or three-dimensional structure) of the input molecule, means that the conformation (or three-dimensional) structure of the output molecule is more likely to match one or more desired properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development).

[0152] In 352, the molecular design engine 110 may encode a three-dimensional representation of the input molecule to generate an embedding of the input molecule. In some exemplary embodiments, the encoder 111 may encode a three-dimensional representation (e.g., a voxelized representation) of the input molecule 152 to generate an embedding 154 of the input molecule 152. One example of this is shown in Figure 1B. In the case of a “seed generation”, the input molecule 152 may be a known molecule (e.g., a molecule from a validation set derived from the PubChem dataset, the QM9 molecular dataset, the Geometric Ensemble of Molecules (GEOM) drug dataset, etc.). In some cases, the known molecule may exhibit one or more undesirable properties. When a known molecule is used as the input molecule 152, the generation process may be initialized with a voxel grid having an atomic density distribution corresponding to the types and positions of atoms expected to be found in the known molecule. Alternatively, the molecular design calculation model 115 may perform de novo generation, in which case the input molecule 152 may be a noise molecule whose atomic types and positions correspond to pure noise (e.g., uniform noise). When a noise molecule is used as the input molecule 152, the generation process can be initialized across the entire voxel grid without any prediction of the type and / or position of atoms. In either case, the type and / or position of atoms in the input molecule 152 may not match those of a molecule exhibiting one or more desired properties (e.g., drug-like properties). Therefore, the molecular design calculation model 115 can be applied to update the three-dimensional representation of the input molecule 152 by updating at least the embedding 154, and to generate an updated embedding 156 such that the corresponding three-dimensional representation of the output molecule 162 can better match the three-dimensional representation of a molecule exhibiting one or more desired properties.

[0153] In some exemplary embodiments, the encoder 111 may encode a three-dimensional representation of the input molecule 152 (e.g., a voxelized representation) by at least downsampling or compressing the three-dimensional representation of the input molecule 152. Doing so may involve condensing at least some of the features present in the three-dimensional representation of the input molecule 152, thereby reducing the dimensionality (or amount of features) present in the three-dimensional representation of the input molecule 152. For example, if the three-dimensional representation of the input molecule 152 includes a [32×32×32] voxel grid containing 32,000 features (or atomic density values), the encoder 111 may condense at least some of those 32,000 features (or atomic density values) to generate a [4×4×4] voxel grid containing 64 features as an embedding 154 of the input molecule 152.

[0154] In some exemplary embodiments, the encoder 111 may generate an embedding 154 of the input molecule 152 with or without downsampling or compression of the three-dimensional representation (e.g., voxelized representation) of the input molecule 152. In some cases, the encoder 111 may implement an identity function, meaning that the embedding 154 may contain the same quantity features (e.g., atomic density values) present in the three-dimensional representation of the input molecule 152. Alternatively, if the embedding 154 is generated by downsampling the voxelized representation of the input molecule 152, doing so may project the voxelized representation of the input molecule 152 from a higher-dimensional discrete voxelized space to a lower-dimensional latent space. Sampling from a lower-dimensional latent space may impose less computational load than directly sampling from a higher-dimensional discrete voxelized space. For example, if sampling from a discrete voxelized space is a resource-intensive task, such as when the input molecule 152 is large (e.g., containing 80 to 200 atoms) or when a large number of candidate molecules are generated from it, the molecular design engine 110 may sample from a potential voxelized space by applying a molecular design calculation model 115 to operate on an embedding 154 of the three-dimensional representation of the input molecule 152. It should be understood that sampling from a potential voxelized space may impose a moderate computational overhead, even when the input molecule 152 is large (e.g., containing 200 or more atoms) or when a large number of candidate molecules are generated.

[0155] In some exemplary embodiments, the encoder 111 may be part of an automated encoder (e.g., a variational autoencoder (VAE) such as a vector quantized variational autoencoder (VQ-VAE)) together with the decoder 119. In some cases, the encoder 111 may be trained to encode a voxelized representation of the input molecule 152 so that the decoder 119 can recover a three-dimensional representation (e.g., a voxelized representation) of the input molecule 152 from the resulting embedding 154. Further explanation is provided, TIFF2026518674000078.tif3170 shows the voxelized representation of the molecule. TIFF2026518674000079.tif5170 indicates encoder 111, TIFF2026518674000080.tif5170 indicates decoder 119, TIFF2026518674000081.tif4170 represents embedding 154. Voxelized molecular representation of input molecule 152, etc. TIFF2026518674000082.tif3170 is a continuous latent embedding according to, for example, formula (2) below. Encoder to generate TIFF2026518674000083.tif6170 It can be encoded as TIFF2026518674000084.tif6170.

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[0156] According to equation (3), each continuous latent embedding TIFF2026518674000086.tif6170 is embedded by nearest neighbor search In the learned shared codebook for TIFF2026518674000087.tif3170 TIFF2026518674000088.tif4170 discrete latent embedding by matching with one of the vectors It can be quantized to TIFF2026518674000089.tif3170.

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[0157] Quantized potential embedding TIFF2026518674000091.tif7170 is a decoder After passing through TIFF2026518674000092.tif5170, the original voxelized molecular representation is obtained according to the following formula (4). TIFF2026518674000093.tif3170 can be reconstructed.

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[0158] In some cases, because the operation is not differentiable, there may be no defined gradient for the nearest neighbor lookup within the codebook of each latent embedding. Instead, the nearest neighbor search within the codebook is performed for each quantized latent embedding Replace TIFF2026518674000100.tif7170 with one of the learned codebook embeddings that has the same dimensions. The stopping gradient (sg) operation is performed by the decoder. Quantized latent embeddings input to TIFF2026518674000101.tif6170 From TIFF2026518674000102.tif7170, before quantization, encoder Continuous latent embedding output by TIFF2026518674000103.tif6170 The gradient can be copied to TIFF2026518674000104.tif6170. The stopping gradient (sg) calculation may function as a forward identity function by simply copying the variables. However, the encoder During the reverse pass of updating the gradient in TIFF2026518674000105.tif6170, the stop gradient (sg) operation can prevent the gradient from flowing through the gradient update for the specific term to which the operation applies, because it cannot calculate the gradient for at least that term.

[0159] In some exemplary embodiments, an encoder forms an automatic encoder (e.g., a variational autoencoder (VAE)). TIFF2026518674000106.tif5170 and decoder The training of TIFF2026518674000107.tif5170 involves reducing (or minimizing) three distinct losses or loss terms in the encoder. TIFF2026518674000108.tif5170 and decoder This may include adjusting TIFF2026518674000109.tif5170. The first loss term is embedded Encoder to generate TIFF2026518674000110.tif4170 Voxelized molecular representation captured by TIFF2026518674000111.tif5170 TIFF2026518674000112.tif3170 and embedded Decoder based on TIFF2026518674000113.tif4170 Reconstruction generated by TIFF2026518674000114.tif5170 It may include a reconstruction loss corresponding to the difference between TIFF2026518674000115.tif4170 (e.g., mean squared error (MSE) reconstruction loss). The second loss term is the embedding vector. TIFF2026518674000116.tif4170 is encoded Sequential latent embeddings output by TIFF2026518674000117.tif5170 The embedding used to quantize the latent space by moving it towards TIFF2026518674000118.tif6170 The codebook learning for TIFF2026518674000119.tif3170 can be performed. The third loss term is the encoder. TIFF2026518674000120.tif5170 is embedded A commitment loss can be quantified to commit to TIFF2026518674000121.tif6170 and ensure that its output does not increase arbitrarily. This third loss term is the commitment cost weight. It may be associated with TIFF2026518674000122.tif5170, and the commitment cost weights may also be hyperparameters set through experimentation. Equation (5) below is the encoder TIFF2026518674000123.tif5170 and decoder Overall loss function for training TIFF2026518674000124.tif5170 This is an example of TIFF2026518674000125.tif6170.

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[0160] In 354, the molecular design engine 110 may generate an updated embedding by at least updating the embedding of the three-dimensional representation of the input molecule. In some exemplary embodiments, the molecular design engine 110 may apply a molecular design calculation model 115 (e.g., denoising model 117) to denoise the three-dimensional representation of the input molecule 152 by updating at least the embedding 154 of the three-dimensional representation of the input molecule 152 and generating an updated embedding 156. For example, in some cases, the three-dimensional representation of the input molecule 152 may contain noise that contributes to a discrepancy between the types and / or locations of atoms present in the input molecule 152 and those of atoms in the molecule exhibiting one or more desired properties (e.g., drug-like properties). In other words, the molecular design calculation model 115 may update the embedding 154 of the three-dimensional representation of the input molecule 152 to increase the likelihood that the resulting output molecule 162 exhibits one or more desired properties. As previously mentioned, the noise removed from the embedding 154 by the denoising model 117 should not be confused with the noise that projects the three-dimensional representation of the input molecule 152 from its true data distribution, which exhibits jagged density transitions, to a noisy data distribution that exhibits smoother density transitions for more efficient sampling (e.g., gradient-based Markov chain Monte Carlo (MCMC) sampling). As will be explained in more detail below, by updating the embedding 154 of the three-dimensional representation of the input molecule 152, the molecular design calculation model 115 (e.g., the denoising model 117) may traverse the smoother density of the noisy data distribution to sample the updated embedding 156 from the increasingly high density region of the noisy data distribution before "jumping" back to the original true data distribution when a sample is selected that indicates a threshold dimension of being within the noisy data distribution.

[0161] In some exemplary embodiments, the denoising model 117 may apply updates to the embedding 154 of the three-dimensional representation of the input molecule 152 that correspond to changes in the types and / or positions of atoms present in the input molecule 152. If the encoder 111 implements an identity function and the embedding 154 is generated without downsampling (or compression) of the underlying three-dimensional representation (e.g., voxelized representation) of the input molecule 152, the denoising model 117 may update the embedding 154 by updating at least the atomic density of one or more voxels in at least one channel of the embedding 154. Alternatively, if the generation of the embedding 154 involves downsampling (or compression) of the underlying three-dimensional representation (e.g., voxelized representation) of the input molecule 152, the denoising model 117 may update the embedding 154 by updating at least one or more values ​​present in the embedding 154, at least a portion of which condense multiple atomic density values ​​contained in the three-dimensional representation (e.g., voxelized representation) of the input molecule 152.

[0162] In some exemplary embodiments, the molecular design calculation model 115 may apply a denoising model 117 to update the embedding 154 of the input molecule 152 based on a function 175. In some cases, the function 175 may output a value (e.g., a score and / or similar) for each sample (or molecule) selected from a noisy data distribution that indicates the likelihood that the sample (or molecule) is in a noisy data distribution. For example, in some cases, the value output by the function 175 for a particular sample (or molecule) may indicate a local change in density where the sample (or molecule) is selected. The denoising model 117 may update the embedding 154 over several consecutive sampling iterations based on at least the values ​​output by the function 175. During each sampling iteration, the denoising model 117 may be applied to further update the embedding 154 so that the resulting updated embedding 156 is selected from a denser region of the noisy data distribution than in the previous sampling iteration.

[0163] In some exemplary embodiments, the molecular design calculation model 115 may perform gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling) of a noisy data distribution, where the embedding 154 of the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 is updated over a series of consecutive sampling iterations, in which case each iteration samples from a progressively increasing density region of the noisy data distribution to increase the likelihood that the resulting updated embedding 156 is in the noisy data distribution. Furthermore, in some cases, the updates made to the embedding 154 of the input molecule 152 may be accumulated over a series of consecutive iterations. To further illustrate, consider an example where the embedding 154 of the three-dimensional representation of the input molecule 152 undergoes a first update and a second update. The molecular design calculation model 115 may apply a function 175 to determine a first value (e.g., a first score) for the embedding 154 with the first update and a second value (e.g., a second score) for the embedding 154 with the second update. If, during subsequent iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling, the first and second values ​​indicate that the embedding 154 with the first update is sampled from a higher density region of the noisier data distribution and is more likely to be in a noisier data distribution than the embedding 154 with the second update, then the denoising model 117 may be applied to further update the embedding 154 with the first update. In some cases, one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling may be performed, in which case the molecular design calculation model 115 applies the denoising model 117 to further modify the embedding 154 of the three-dimensional representation (e.g., voxelized representation) of the input molecule 152 until one or more criteria are met. For example, in some cases, the molecular design calculation model 115 may perform one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling until a threshold amount of sampling iterations have been performed.Alternatively and / or additionally, the molecular design calculation model 115 may perform one or more additional iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling on the updated embedding 156 until the function 175 outputs values ​​(e.g., scores and / or similar) that satisfy one or more thresholds. The satisfaction of one or more thresholds for values ​​(e.g., scores and / or similar) associated with the updated embedding 156 may indicate that the updated embedding 156 is selected from a region of a noisy data distribution with a sufficiently high density, and that the likelihood of the updated embedding 156 being within the noisy data distribution satisfies one or more thresholds. In some cases, one or more criteria may also include generating an output molecule of a threshold quantity exhibiting one or more desired properties (e.g., at least one output molecule exhibiting a threshold level for one or more drug-like properties such as affinity, specificity, biological activity, or developability).

[0164] In 356, the molecular design calculation model 115 can decode the updated embedding to generate a noisy three-dimensional representation of the output molecule. In some exemplary embodiments, the molecular design engine 110 can apply the molecular design calculation model 115 (e.g., denoising model 117) to update the embedding 154 of the three-dimensional representation of the input molecule 152, generating the updated embedding 156. Then, the decoder 119 can be applied to decode the updated embedding 156 to generate a noisy three-dimensional representation 158 of the output molecule 162. Decoding the updated embedding 156 can map the updated embedding 156 from a latent voxelized space occupied by embeddings of the three-dimensional representations of various molecules to a latent discrete space. However, as will be explained in more detail below, the latent discrete space may be a noisy latent space, which means that the noisy three-dimensional representation 158 generated by the decoder 119 that decodes the updated embedding 156 may require further denoising in order to project the noisy three-dimensional representation 158 back to the true data distribution of molecules exhibiting one or more desired properties.

[0165] In some exemplary embodiments, the decoder 119 of the molecular design engine 110 may generate a noisy three-dimensional representation 158 by decoding an updated embedding 156 generated by the molecular design computation model 115 (e.g., the denoising engine 117). As previously mentioned, in some cases, the decoder 119 may, together with the encoder 111, form part of an autoencoder (e.g., a variational autoencoder such as a vector quantized variational autoencoder (VQ-VAE)). In some cases, the encoder 111 and the decoder 119 may be trained in parallel, and the encoder 111 may be trained to generate embeddings of three-dimensional representations of molecules (e.g., voxelized representations), such as an embedding 154 of the three-dimensional representation of the input molecule 152, from which the decoder 119 can recover the original three-dimensional representation (e.g., voxelized representation). Thus, once the updated embedding 156 is generated, the decoder 119 can be applied to recover a noisy three-dimensional representation 158 of the output molecule 162 from which.

[0166] In some cases, decoding the updated embedding 156 may involve upsampling (or decompressing) the updated embedding 156, which can then be projected back from the potential voxelization space to the discrete voxelization space. The noisy three-dimensional representation 158 (e.g., the noisy voxelized representation) of the output molecule 162 may exhibit the same dimensionality (or number of features) as the three-dimensional representation (e.g., the voxelized representation) of the input molecule 152 ingested by the molecular design engine 110 in operation 352. For example, in some cases, the three-dimensional representation of the input molecule 152 may contain a [32×32×32] voxel grid, meaning that the three-dimensional representation of the input molecule 152 may contain 32,000 features (or atomic density values). On the other hand, each of the embedding 154 on which the molecular design calculation model 115 operates and the resulting updated embedding 156 may contain a [4×4×4] voxel grid with 64 features. In some cases, the decoder 119 may decode the updated embedding 156 by upsampling (or decompressing) the [4×4×4] voxel grid contained therein to generate a [32×32×32] voxel grid for a noisy three-dimensional representation 158 (e.g., a noisy voxel representation) of the output molecule 162. It should be understood that this upsampling (or decompression) may recover 32,000 features (or atomic density values) present in the noisy three-dimensional representation 158 (e.g., a voxel representation) of the output molecule 162. As mentioned above, these 32,000 features (or atomic density values) may indicate the positions of various atoms present in the output molecule 162. Furthermore, the 32,000 features (or atomic density values) may extend to one or more channels, each corresponding to a type of atom that may be present in the output molecule 162.

[0167] In 358, the molecular design engine 110 may denoise a noisy three-dimensional representation of the output molecule to generate a three-dimensional representation of the output molecule. In some exemplary embodiments, the denoising engine 117 of the molecular design calculation model 115 may generate a three-dimensional representation (e.g., a voxelized representation) of the output molecule 162 by at least denoising a noisy three-dimensional representation 158 generated by a decoder 119 that decodes the updated embedding 156. As previously mentioned, in some cases, the molecular design calculation model 115 (e.g., the denoising model 117) may generate an updated embedding 156 over one or more iterations of a gradient-based Markov chain Monte Carlo (e.g., Langevin-Markov chain Monte Carlo method). In doing so, the molecular design calculation model 115 can traverse the noisy latent distribution based on at least the output of function 175 (e.g., the score output by function 175) to sample updated embeddings 156 from high-density regions of the noisy latent distribution that are occupied by embeddings of three-dimensional representations of molecules that are more likely to exhibit one or more desired properties (e.g., drug-like properties). However, decoding the updated embeddings 156 only maps the updated embeddings 156 from the latent voxelized space to the discrete voxelized space, while the noisy three-dimensional representations 158 still occupy the noisy data distribution and not the true data distribution of molecules exhibiting one or more desired properties. Therefore, in some cases, a recovery model 118 can be applied to map the noisy three-dimensional representations 158 from the noisy data distribution to the true data distribution. In some cases, this may constitute a “jump” back to the true data distribution, meaning that the three-dimensional representations of the output molecules 162 generated therefrom occupy the true data distribution.

[0168] In some cases, the recovery model 118 may share the same architecture (e.g., an artificial neural network (ANN)) as the denoising model 117, which is trained to denoise an embedding 154 of the three-dimensional representation of the input molecule 152 by traversing a noisy latent distribution and generate an updated embedding 156. However, as mentioned above, the recovery model 118 may be trained to denoise different types. Thus, in some cases, the recovery engine 118 may be trained on a training dataset to denoise a noisy three-dimensional representation 182 of a sample molecule and recover the original three-dimensional representation 182 from it. In contrast, the denoising engine 117 may be trained to recover an embedding 186 of the noisy three-dimensional representation 182 of the sample molecule from a corrupted embedding 188. In this regard, training the denoising engine 117 may involve adjusting one or more parameters of the denoising engine 117 (e.g., an artificial neural network (ANN)) to reduce (or minimize) the difference (e.g., mean squared error (MSE)) between the original three-dimensional representation of the sample molecule that the denoising engine 117 recovers from the noisy three-dimensional representation of the sample molecule and the three-dimensional representation of the sample molecule.

[0169] To further explain, the quantized latent embedding described in operation 252 Let's consider TIFF2026518674000127.tif7170. As mentioned earlier, quantized latent embeddings TIFF2026518674000128.tif7170 is a voxelized molecular representation. Encoder for encoding TIFF2026518674000129.tif3170 It can be generated by TIFF2026518674000130.tif6170. In some cases, quantized latent embeddings Noise in TIFF2026518674000131.tif7170 TIFF2026518674000132.tif3170 (e.g., Gaussian noise such as isotropic Gaussian noise) may be added. For example, in some cases a fixed large noise level Noise with an identity-covariance matrix scaled to TIFF2026518674000133.tif3170 TIFF2026518674000134.tif3170 (e.g., Gaussian noise such as isotropic Gaussian noise) may be added according to the following equation (6).

[0170]

number

[0171] Latent model The noise reduction engine 117, which can be represented as TIFF2026518674000136.tif6170, The original potential embedding of TIFF2026518674000137.tif3170 before the addition (without the addition). TIFF2026518674000138.tif7170 and denoised potential embeddings generated by denoised engine 117 While reducing (or minimizing) the reconstruction loss (e.g., mean squared error (MSE) reconstruction loss) between TIFF2026518674000139.tif7170 and latent embeddings, TIFF2026518674000140.tif7170 can be trained to denoise and recover. Denoised potential embeddings Latent model to generate TIFF2026518674000141.tif7170 The denoising performed by TIFF2026518674000142.tif6170 is shown in equation (7) below. On the other hand, equation (8) shows the latent model Loss function for training TIFF2026518674000143.tif6170 This shows TIFF2026518674000144.tif6170, which is noise. The original potential embedding of TIFF2026518674000145.tif3170 before (or without) the addition. TIFF2026518674000146.tif7170 and denoised potential embeddings This includes reducing (or minimizing) the difference (e.g., mean squared error (MSE)) between TIFF2026518674000147.tif7170 and the original.

number

number

[0172] In 360, the molecular design engine 110 may generate one or more other representations of the output molecule based on at least a three-dimensional representation of the output molecule. In some exemplary embodiments, the molecular design engine 110 may generate one or more other representations of the output molecule 162 based on at least a voxelized representation of the output molecule 162, including, for example, a one-dimensional representation of the output molecule 162 (e.g., a Simplified Molecular Input Line Input System (SMILES) string), a two-dimensional representation of the output molecule 162 (e.g., a molecular graph), and so on. For example, in some cases, the molecular design calculation model 110 may recover the positions (e.g., coordinates) of atoms present in the output molecule 162 and the bonds between them from the voxelized representation of the output molecule 162. In some cases, the molecular design engine 110 may apply a peak detection technique to determine the positions (e.g., coordinates) of atoms present in the output molecule 162 based on one or more peaks in the atomic density contained in the voxelized representation of the output molecule 162, before determining one or more interconnection bonds based on the positions of the atoms. Alternatively, the molecular design engine 110 may apply a machine learning model trained to convert the voxelized representations of the output molecules 162 into one or more other representations.

[0173] As described above, in some exemplary embodiments, the molecular design calculation model 115, including the denoising model 117, may operate on a three-dimensional representation of a molecule instead of a one-dimensional or two-dimensional representation of the molecule, because realistic and effective molecules exhibiting certain desired properties are likely to be generated based on a representation of the molecule that captures its composition (e.g., constituent atoms) and conformation (or three-dimensional structure). In some cases, the molecular design calculation model 115, including the denoising model 117, may operate on a voxelized representation of a molecule. Unlike conventional three-dimensional representations of molecules (e.g., point cloud representations), a voxelized representation of a molecule can represent both the type and position of atoms as one or more continuous (e.g., Gaussian) distributions across a voxel grid centered on the atomic coordinates of individual atoms. Therefore, unlike conventional three-dimensional representations of molecules (e.g., point cloud representations), the molecular design calculation model 115 can apply the denoising model 117 to work on voxelized representations of input molecules without requiring any workarounds to match various types of data distributions (e.g., discrete distributions of atomic types and continuous distributions of atomic positions), nor without requiring prior knowledge of the number of atoms present in the resulting output molecule.

[0174] To further illustrate, Figure 4 shows examples of voxelized representations and corresponding two-dimensional representations of different molecules according to several exemplary embodiments. For example, Figure 4 shows a voxelized representation 400 and a two-dimensional representation 450 of the molecule. In some exemplary embodiments, the voxelized representation 400 of the molecule may be generated by dividing (or discretizing) the three-dimensional space around the constituent atoms into a voxel grid 410, where each type of atom (or element) present in the molecule is represented by a different grid channel. This division (or discretization) is performed by TIFF2026518674000150.tif3170 voxelized molecules TIFF2026518674000151.tif6170, TIFF2026518674000152.tif7170, You can also generate TIFF2026518674000153.tif6170, where, TIFF2026518674000154.tif4170 shows the length of each grid edge. TIFF2026518674000155.tif3170 represents the number of channels (e.g., the amount of different types of atoms (or elements)) in the dataset.

[0175] In some cases, the voxel grid 410 may be a three-dimensional grid of voxels organized into continuous layers of rows and columns. Each voxel in the voxel grid 410 may be a volume element, such as a three-dimensional cube, formed at the intersection of rows and columns. Furthermore, each voxel in the voxel grid 410 may have a value (e.g., value) indicating the atomic density at the corresponding location. It may be associated with TIFF2026518674000156.tif6170. For a single molecule, the corresponding voxelized representation may be a box around the center of the molecule which is then divided into voxels. To generate the voxelized representation 400 of a molecule, each constituent atom may be converted to a three-dimensional continuous (e.g., Gaussian) density according to the following formula (9). For example, the example of the voxel grid 410 shown in Figure 4 may include a first atomic density 415a representing a first atom of a first type and a second atomic density 415b representing a second atom of a second type.

number

number

[0176] As mentioned, in some cases, the atomic density within the voxelized representation 400 of the molecule may be concentrated around the atoms present within the molecule. Therefore, occupancy TIFF2026518674000172.tif7170 can take a maximum value (e.g., a value of 1) at the center of the atom and decrease to a minimum value (e.g., a value of 0) as the distance from the center of the atom increases. All channels within the voxel grid may be independent; that is, channels do not share interactions or volume contributions. In some cases, the size of the voxel grid 410 contained in the voxelized representation 400 of a molecule may correspond to the size of the molecule being represented (e.g., the number of constituent atoms). For example, in some cases, the voxel grid 410 may be a [32×32×32] voxel grid if the molecule has fewer atoms (e.g., the QM9 molecular dataset) and a [64×64×64] voxel grid if the molecule has more atoms (e.g., the Geometric Ensemble of Molecules (GEOM) drug dataset). Furthermore, in some cases, the number of channels within the voxelized representation 400 of a molecule may correspond to the number of atomic types (or elements) present in the molecule. For example, the voxelized representation of molecules in the QM9 molecular dataset may contain five channels for the five types of atoms that make up those molecules (e.g., carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and fluorine (F)). On the other hand, the voxelized representation of molecules in the Geometric Ensemble of Molecules (GEOM) drug dataset may contain eight channels for the eight types of atoms present in those molecules (e.g., carbon (C), hydrogen (H), oxygen (O), nitrogen (N), fluorine (F), sulfur (S), chlorine (Cl), and bromine (Br)). Therefore, the voxelized representation of each molecule in the QM9 molecular dataset is: TIFF2026518674000173.tif7170 may include a voxel grid, and the voxelized representation of each molecule in a molecular geometric ensemble (GEOM) drug dataset is: TIFF2026518674000174.tif7170 may contain a voxel grid.

[0177] As described above, in some exemplary embodiments, the molecular design calculation model 115, including the denoising model 117, may be trained to approximate and then sample from the noisy data distribution of a noisy voxelized representation of a molecule, or possibly a noisy embedding of the noisy voxelized representation of a molecule, instead of the true data distribution of the voxelized representation of a molecule that is not perturbed by noise. Training the denoising model 117 to approximate the noisy data distribution of a molecule, such as the noisy data distribution of a noisy voxelized representation of a molecule exhibiting a particular desired property (e.g., drug-like property) or its noisy embedding, may involve determining the function 175 such that for each voxelized representation (or its noisy embedding) of a molecule sampled from the noisy data distribution, the function 175 outputs a value indicating the density of the corresponding location in the noisy data distribution. If the function 175 is a scoring function, the function 175 may output a score corresponding to a local change in the density (or gradient) of the noisy data distribution. Therefore, if function 175 is a scoring function, the score output by function 175 for a noisy voxelized representation (or its noisy embedding) of the numerator may indicate a local change in density at the corresponding location in the noisy data distribution.

[0178] In some cases, the denoising engine 117 may be trained to denoise noisy voxelized representations of molecules, or possibly noisy embeddings of such representations, generated by the molecular design calculation model 115 (e.g., the denoising model 117). For further illustration, Figure 5A shows a schematic diagram illustrating an example of training the denoising engine 117 to denoise noisy voxelized representations of molecules according to several exemplary embodiments. As shown in Figure 5A, the training dataset for training the denoising engine 117 may be generated to contain multiple training samples, each corresponding to a sample molecule. For example, Figure 5A shows a sample molecule 500, which may be a known molecule from the PubChem dataset, the QM9 molecular dataset, or the Geometric Ensemble of Molecules (GEOM) drug dataset. The sample molecule 500 may be rendered in a one-dimensional representation (e.g., a Simplified Molecular Input Line Input System (SMILES) string) or a two-dimensional representation (e.g., a molecular graph), neither of which adequately captures the conformation (or three-dimensional structure) of the sample molecule 500. Therefore, in some cases, a one-dimensional or two-dimensional representation of sample molecule 500 can be converted to a three-dimensional representation of sample molecule 500 in order to generate training samples to be included in the training dataset. For example, in some cases, the one-dimensional or two-dimensional representation of sample molecule 500 can be converted to the voxelized representation shown in Figure 5A. It can be converted to TIFF2026518674000175.tif4170. Voxelized representation of 500 sample molecules. TIFF2026518674000176.tif4170 can represent both the type and position of atoms present in sample molecule 500 as one of a more continuous (e.g., Gaussian) density across a voxel grid, centered on the individual atoms present in sample molecule 500.

[0179] Referring again to Figure 5A, in some cases, the voxelized representation of sample molecule 500 is shown. TIFF2026518674000177.tif4170 is a noisy voxelized representation. To generate TIFF2026518674000178.tif4170, the noise level TIFF2026518674000179.tif3170 may contain noise. The noise can be mixed with TIFF2026518674000180.tif3170 (for example, Gaussian noise such as isotropic Gaussian noise). The addition of TIFF2026518674000181.tif3170 reveals the true data distribution occupied by the clean (or original) voxelized representation of the molecule. From TIFF2026518674000182.tif6170, a noisy data distribution dominated by noisy voxelized representations of molecules. Voxelized representation in TIFF2026518674000183.tif6170 TIFF2026518674000184.tif4170 can be projected. As mentioned above, molecular design calculation model 115 is a voxelized representation of 500 sample molecules. True data distribution such as TIFF2026518674000185.tif4170 When working directly on the clean (or original) voxelized representation of molecules from TIFF2026518674000186.tif6170, the true data distribution The jagged energy landscape of TIFF2026518674000187.tif6170 is such that when sampling from it, molecular design calculation model 115 does not represent the true data distribution. This can prevent proper searching of TIFF2026518674000188.tif6170. In contrast, a noisy data distribution... TIFF2026518674000189.tif6170 may show a smoother energy landscape with gentler gradient changes, which is a result of molecular design calculation model 115 having a noisy data distribution. Sampling from TIFF2026518674000190.tif6170 means that greater diversity may be obtained in the resulting output molecules. Therefore, in some cases, the denoising engine 117 may be able to handle noisy data distributions. The noisy voxelized representations of 500 sample molecules can be applied to denoise the noisy voxelized representations of molecules generated by molecular design calculation model 115, which samples from TIFF2026518674000191.tif6170. It can be trained to denoise noisy voxelized representations of molecules, such as TIFF2026518674000192.tif4170. As will be explained in more detail below, in some cases, the voxelized representations of 500 sample molecules can be denoised. TIFF2026518674000193.tif4170 is noise TIFF2026518674000194.tif3170 may undergo downsampling (or compression) before being added, which means that the denoising engine 117 can be trained to denoise the noisy embedding of the molecule's voxelized representation instead of the noisy voxelized representation of the molecule shown in Figure 5A.

[0180] Referring again to Figure 5A, the noise reduction engine 117 removes the noise from the voxelized representation. TIFF2026518674000195.tif4170 may be trained to denoise. In some cases, the denoising engine 117 may produce a corresponding clean voxelized representation. Noisy voxelized representation of TIFF2026518674000196.tif4170 by recovering at least from it TIFF2026518674000197.tif4170 may be trained to denoise. For example, in some cases, the denoising engine 117 may denoise noisy voxelized representations. It may also be an encoder-decoder three-dimensional convolutional neural network (CNN) trained to map noisy voxels in TIFF2026518674000198.tif4170 to corresponding clean voxels. In doing so, the denoising engine 117 can clean the voxelized representation. Denoised voxelized representation approximating TIFF2026518674000199.tif4170 TIFF2026518674000200.tif5170 may be generated. For example, in some cases, training of the denoising engine 117 may result in a denoised voxelized representation. Clean voxelized representation corresponding to TIFF2026518674000201.tif5170 This may include adjusting the parameters of the denoising engine 117 to reduce (or minimize) the difference (e.g., mean squared error (MSE)) between TIFF2026518674000202.tif4170 and the result. In some cases, voxelized molecular representation Noise added to TIFF2026518674000203.tif4170 Noise level that determines the amount of TIFF2026518674000204.tif3170 TIFF2026518674000205.tif3170 may be set as a hyperparameter of the noise reduction engine 117. Furthermore, in some cases, the noise level TIFF2026518674000206.tif3170 can be kept fixed (or constant) during training of the denoising engine 117, reducing the complexity of the training process compared to diffusion models. Unlike natural images, voxelized representations contain more structural information on sample molecules 500 than texture information. Due to the nature of TIFF2026518674000207.tif4170, one-step denoising (as opposed to diffusion over multiple time steps) is applied to the original voxelized representation. Please understand that this may be sufficient to reconstruct TIFF2026518674000208.tif4170.

[0181] In some exemplary embodiments, the molecular design calculation model 115 may apply a denoising model 117 to generate a voxelized representation of the output molecule by denoising at least the noisy voxelized representation of the input molecule over one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling). In some cases, the denoising model 117 may denoise the noisy data distribution You can also sample from TIFF2026518674000209.tif6170, which has a noisy data distribution. TIFF2026518674000210.tif5170 shows a noisy data distribution. This involves traversing towards a gradually increasing density region of TIFF2026518674000211.tif6170, where this region is occupied by molecules exhibiting one or more desired properties (e.g., drug-like properties). For further explanation, Figure 5B shows a noisy data distribution. The traverse of TIFF2026518674000212.tif5170 is a sampling iteration. Sample (or molecule) in TIFF2026518674000213.tif6170 Sampling iterations of TIFF2026518674000214.tif6170 Sample (or molecule) in TIFF2026518674000215.tif4170 TIFF2026518674000216.tif4170, and sampling iterations Sample (or molecule) in TIFF2026518674000217.tif6170 This indicates that selecting TIFF2026518674000218.tif6170 is included. In some cases, traversing a noisy data distribution may result in sample TIFF2026518674000219.tif6170 is a sample. A noisy data distribution in a significantly higher density region than TIFF2026518674000220.tif4170. While samples are sampled from TIFF2026518674000221.tif6170, TIFF2026518674000222.tif4170 is a sample. Noisy data distribution in the higher density region than TIFF2026518674000223.tif6170 The sampling iterations may be derived by function 175, as sampled from TIFF2026518674000224.tif6170. In some cases, each iteration of a gradient-based Markov chain Monte Carlo (MCMC) method may involve further modification of the sample (or numerator) selected during the previous iteration. Thus, the sampling iterations are as shown below. Noisy data distribution in TIFF2026518674000225.tif6170 Sample selected from TIFF2026518674000226.tif6170 TIFF2026518674000227.tif6170 is the previous sampling iteration. Selected sample in TIFF2026518674000228.tif4170 It can be generated based on TIFF2026518674000229.tif4170. Equation (10) below is for noisy data distribution This represents the traverse of TIFF2026518674000230.tif6170.

number

[0182] Referring again to Figure 5B, in some cases, the noise removal engine 117 The corresponding noisy voxelized representation selected from TIFF2026518674000238.tif6170 When removing noise from TIFF2026518674000239.tif4170, the molecule The voxelized representation of TIFF2026518674000240.tif6170 can be generated. As described above, the noisy voxelized representation The noise removal of TIFF2026518674000241.tif4170 is, for example, a least squares estimator By applying TIFF2026518674000242.tif7170, the noisy voxelized representation TIFF2026518674000243.tif4170 can be projected back onto the true data distribution TIFF2026518674000244.tif6170. This constitutes the "jump" shown in Figure 5B. Further, in the example shown in Figure 5B, the noise removal model 117 is applied to traverse the noisy data distribution TIFF2026518674000245.tif6170 and select samples therefrom while performing the "jump" back to the true data distribution TIFF2026518674000246.tif6170 in each sampling iteration. For example, the molecule The noisy data distribution in TIFF2026518674000247.tif6170 during the sampling iteration Sample selected from TIFF2026518674000248.tif6170 TIFF2026518674000249.tif6170 has been denoised to reveal the true data distribution. It can be generated when projected back to TIFF2026518674000250.tif6170, but the molecule TIFF2026518674000251.tif5170 is a subsequent sampling iteration. Noisy data distribution in TIFF2026518674000252.tif6170 Sample selected from TIFF2026518674000253.tif6170 TIFF2026518674000254.tif4170 has been denoised to reveal the true data distribution. This can be generated when projected back to TIFF2026518674000255.tif6170.

[0183] [Table 1]

[0184] In some exemplary embodiments, the denoising model 117 is used for noisy data distributions. The TIFF2026518674000257.tif6170 can be traversed, and samples can be selected from it until one or more criteria are met. For example, the denoising model 117 will perform a threshold amount of sampling iterations at that point. It may continue traversing the energy landscape of noisy data distributions up to TIFF2026518674000258.tif6170. Alternatively and / or additionally, denoising model 117 samples TIFF2026518674000259.tif6170 has a noisy data distribution. When showing the dimensions of the threshold in TIFF2026518674000260.tif6170, Noisy data distribution until TIFF2026518674000261.tif6170 is selected We can continue traversing the energy landscape of TIFF2026518674000262.tif6170. For further explanation, Figure 5C shows a noisy data distribution including, for example, samples 510a-510f. The denoising model 117 applied to select multiple consecutive samples from TIFF2026518674000263.tif6170 is shown. In the example shown in Figure 5C, sampling (e.g., gradient-based Markov chain Monte Carlo (MCMC) sampling) is applied to a noisy data distribution. First sample from TIFF2026518674000264.tif6170 To select TIFF2026518674000265.tif6170, we can start with molecular design calculation model 115 which applies denoising model 117. In some cases, the first sample The selection of TIFF2026518674000266.tif6170 may include denoising model 117 updating the noisy voxelated representation of the corresponding molecule (or its noisy embedding).

[0185] As shown in Figure 5C, the first sample Denoising TIFF2026518674000267.tif6170 and the corresponding voxelized representation This can generate TIFF2026518674000268.tif7170. This denoising operation is for noisy data distributions. True data distribution from TIFF2026518674000269.tif6170 This may constitute a “jump” to TIFF2026518674000270.tif6170. Each subsequent sampling iteration may include a denoising model 117 applied to further update the noisy voxelized representation of the molecules selected during the previous sampling iteration. In the example shown in Figure 5C, the molecular design calculation model 115 is a noisy data distribution From TIFF2026518674000271.tif6170 The denoising model 117 can be continued to be applied until 170 consecutive samples are selected in TIFF2026518674000272.tif4. Sample of TIFF2026518674000273.tif4170 TIFF2026518674000274.tif4170 is the corresponding voxelized representation To generate TIFF2026518674000275.tif5170, the data may be denoised, for example, by a denoising engine 117. In doing so, the noisy data distribution can be reduced. From TIFF2026518674000276.tif6170 Sample of TIFF2026518674000277.tif4170 TIFF2026518674000278.tif4170 represents the true data distribution It can be restored to TIFF2026518674000279.tif6170. The values ​​in TIFF2026518674000280.tif4170 represent the number of sampling iterations and the noisy data distribution. It should be understood that the number of samples selected from TIFF2026518674000281.tif5170 can be determined. Increasing the value of TIFF2026518674000282.tif4170 may increase the number of updates performed on the initial input molecule (e.g., the "seed" molecule). A higher value for TIFF2026518674000283.tif4170 may increase the difference between the initial input molecule (e.g., the "seed" molecule) and the final output molecule, as well as the novelty of the final output molecule.

[0186] In some exemplary embodiments, a noisy data distribution From TIFF2026518674000284.tif6170 Sample of TIFF2026518674000285.tif4170 Select TIFF2026518674000286.tif4170 and the sample of TIFF2026518674000287.tif4170 Denoise TIFF2026518674000288.tif4170 to obtain the corresponding voxelized representation When generating TIFF2026518674000289.tif5170, the molecular design engine 110 can generate one or more other representations based on the voxelized representation TIFF2026518674000290.tif5170. For example, in some cases, the molecular design engine 110 can generate a one-dimensional representation (e.g., a Simplified Molecular-Input Line-Entry System (SMILES) string) and / or a two-dimensional representation (e.g., a molecular graph) of the corresponding molecule based at least on the voxelized representation TIFF2026518674000291.tif5170.

[0187] FIG. 5D depicts a schematic diagram showing an example of a process for generating other molecular representations from the voxelized representation TIFF2026518674000292.tif5170 according to some exemplary embodiments. In the example shown in FIG. 5D, the molecular design engine 110 can determine the atoms present in the corresponding molecule by at least identifying peaks (e.g., atom density values that meet one or more thresholds) within the voxelized representation TIFF2026518674000293.tif5170. Further, the molecular design engine 11 can determine one or more bonds that interconnect the atoms present in the molecule. The one-dimensional or two-dimensional display of the molecule can be generated based at least on the atoms and interconnecting bonds. Alternatively, in some cases, the molecular design engine 110 can apply a machine learning model trained to convert the voxelized representation TIFF2026518674000294.tif5170 into one or more other representations of the corresponding molecule.

[0188] In some exemplary embodiments, instead of operating in a noisy discrete voxelized space, as shown in Figures 5A to 5D, the molecular design calculation model 115 may operate in a noisy latent voxelized space. For example, in some cases, a noisy voxelized representation Instead of applying denoising model 117 to denoise TIFF2026518674000295.tif4170 in molecular design calculation model 115, apply denoising model 117 to the voxelized representation. The noisy embedding in TIFF2026518674000296.tif4170 can be denoised. To further illustrate, Figure 6 shows a schematic diagram illustrating an example of the process by which the molecular design calculation model 115 generates a voxelized representation of a molecule by operating in a noisy potential voxelized space, according to several exemplary embodiments. Referring to Figure 6, an input molecule 600, which can be rendered in a one-dimensional or two-dimensional representation, can be transformed into a three-dimensional representation of the input molecule 152. In some cases, the three-dimensional representation of the input molecule 152 may also be a voxelized representation of the input molecule 152, representing the types and positions of atoms within the input molecule 152 together as one or more continuous distributions of atomic density across a voxel grid. In some cases, instead of applying the denoising model 117 to directly act on the noisy voxelized representation of the input molecule 152, the encoder 111 performs noise reduction. Before TIFF2026518674000297.tif3170 is added to the embedding 154 of the voxelized representation of the input molecule 152, the embedding 154 of the voxelized representation of the input molecule 152 may be generated first. The resulting noisy embedding 156 may undergo one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin-Markov chain Monte Carlo (MCMC) sampling). For example, each iteration of gradient-based Markov chain Monte Carlo (MCMC) sampling may include a molecular design calculation model 115 that applies a denoising model 117 to denoise the noisy embedding 156 by at least updating the noisy embedding 156. As mentioned above, updating the noisy embedding 156 in this way is equivalent to selecting one or more samples from a noisy data distribution occupied by the noisy embedding of voxelized representations of molecules exhibiting one or more desired properties. Sampling may be induced by a function (e.g., a score function) such that successive samples are selected from increasingly dense regions of a noisy data distribution, which is likely to be occupied by noisy embeddings of voxelized representations of molecules exhibiting one or more desired properties.

[0189] Referring again to Figure 6, the molecular design calculation model 115 may generate an updated embedding 156 by updating the embedding 154 of the voxelized representation of the input molecule 152 at least over one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling. As shown in Figure 6, the embedding 154 may be denoised by, for example, a denoising engine 117, thereby generating the updated embedding 156. Denoising the embedding 154 may involve sampling the updated embedding 156 from a noisy latent distribution of molecules exhibiting one or more desired characteristics. Furthermore, as shown in Figure 6, the decoder 119 may decode the updated embedding 156 to generate the voxelized representation of the corresponding output molecule 162. Decoding the updated embedding 156 may involve projecting the updated embedding 156 back from the latent voxelized space to the discrete voxelized space. The resulting voxelized representation of the output molecule 162 may be further transformed into a reconstructed molecule 650. It should be understood that the reconstructed molecule 650 can correspond to either a one-dimensional representation of the output molecule (e.g., a Simplified Molecular Input Line Input System (SMILES) string) or a two-dimensional representation (e.g., a molecular graph).

[0190] In some exemplary embodiments, the generation performance of the molecular design calculation model 115 may be evaluated based on various metrics, some of which are listed in Table 2 below.

[0191] [Table 2] JPEG2026518674000299.jpg132170

[0192] In some exemplary embodiments, the generation performance of the molecular design calculation model 115 is, for example, noise level TIFF2026518674000300.tif3170, difference in sampling iteration count TIFF2026518674000301.tif4170 and one or more factors including the radius of atomic density within the voxelized molecular representation may depend. Figure 7 shows different levels of voxelization in the voxelized representation of molecules manipulated by molecular design calculation model 115. Noise in TIFF2026518674000302.tif3170 The stability and uniqueness of molecules generated by molecular design calculation model 115 when Gaussian noise (e.g., isotropic Gaussian noise) is added (Figure 7(a)), total atomic variation and total bond variation (Figure 7(b)), and bond valency are shown. TIFF2026518674000304.tif7170 and joint angles Noise level for TIFF2026518674000305.tif7170 (Figure 7(c)) A graph showing the effect of TIFF2026518674000306.tif3170 is shown. As previously mentioned, unlike the diffusion model, according to the various exemplary embodiments described herein, the noise level TIFF2026518674000307.tif3170 may be fixed during training and sampling. Furthermore, the noise level It should be understood that TIFF2026518674000308.tif3170 is a hyperparameter that imposes a trade-off between sampling quality (e.g., gradient-based Markov chain Monte Carlo (MCMC) sampling) and denoising (e.g., empirical Bayesian framework). In some cases, molecular design engine 110 adds noise to the voxelized representation of the molecule, which denoising engine 117 can still learn to denoise. Noise level to match the maximum amount of TIFF2026518674000309.tif3170 TIFF2026518674000310.tif3170 can be determined. For example, in some cases, the molecular design calculation model 115 and the noise reduction engine 117 can determine various noise levels. The model may be trained on the QM9 molecular dataset at TIFF2026518674000311.tif6170, with other hyperparameters kept constant. The graphs in Figures 7(a), (b), and (c) show that several metrics are higher noise levels. The image quality improves with TIFF2026518674000312.tif3170, but the noise level is higher. As TIFF2026518674000313.tif3170 increases, the molecular stability and bond valence... TIFF2026518674000314.tif7170 indicates a decrease in performance. For the QM9 molecular dataset, the best overall performance across all metrics is achieved with a noise level of 0.9. This is achieved in TIFF2026518674000315.tif3170.

[0193] In some exemplary embodiments, the number of sampling iterations performed as part of a gradient-based Markov chain Monte Carlo method (MCMC) is TIFF2026518674000316.tif4170 may affect the novelty of molecules generated by molecular design calculation model 115. This phenomenon is shown in Figure 8, and it occurs with a different number of sampling iterations. Figure 8 shows molecules output by molecular design computation model 115 (trained on the Geometric Ensemble of Molecules (GEOM) drug dataset) which updates noise molecules (for de novo generation) and known molecules (for seed generation) over TIFF2026518674000317.tif4170. For example, Figure 8 shows a voxelized representation of the first molecule 810 generated by molecular design computation model 115, with noise molecules (for de novo generation) denoised over k=10 sampling iterations; a voxelized representation of the first molecule 820 generated by molecular design computation model 115, with noise molecules (for de novo generation) denoised over k=50 sampling iterations; and a voxelized representation of the third molecule 830 generated by molecular design computation model 115, with noise molecules (for de novo generation) denoised over k=100 sampling iterations.

[0194] In addition to the novelty of the molecules generated by molecular design calculation model 115, the number of sampling iterations Adjusting TIFF2026518674000318.tif4170 may also affect other aspects of the generation performance of molecular design calculation model 115. Table 3 below shows the results for different sampling iteration counts. This study compares the generation performance of molecular design calculation model 115 in TIFF2026518674000319.tif4170 with the generation performance of a conventional generation model EDM that performs 1,000 diffusion steps for generation. The results in Table 3 show that molecular design calculation model 115 performs better with respect to the number of iterations or samples. As TIFF2026518674000320.tif4170 increases, it shows better performance in several metrics. As expected, the average time (in seconds) consumed to generate each molecule is equal to the number of sampling iterations. As TIFF2026518674000321.tif4170 increases, the performance increases linearly. However, molecular design calculation model 115 remains faster than EDM even with 500 sampling iterations. In particular, with just 50 sampling iterations, molecular design calculation model 115 is already better than EDM for most metrics, but on average an order of magnitude faster.

[0195] [Table 3]

[0196] In some exemplary embodiments, the generation performance of the molecular design calculation model 115 may also be influenced by the size of the atomic radius in the voxelized representation on which the molecular design calculation model 115 operates. It should be understood that the size of the atomic radius can change while the resolution of the voxel grid remains fixed (e.g., 25 Å). The generation performance of the molecular design calculation model 115 may peak at a particular atomic radius, even with different hyperparameters. For example, when the molecular design calculation model 115 is applied to act on a voxelized representation with an atomic radius, 25, 5, 75, and 1.0 are fixed radii. 5 consistently outperformed the other values ​​as the hyperparameters of the molecular design calculation model 115 changed.

[0197] In some exemplary embodiments, the generation performance of molecular design calculation model 115 can be compared to existing generative models operating on conventional three-dimensional molecular representations, such as GSchNet, a point cloud autoregressive model, and EDM, a point cloud diffusion-based model. Each model is applied to generate 10,000 samples, which are then analyzed for atomic stability, molecular stability, validity, uniqueness, total atomic variability (TV), total bond variability (TV), and bond valency. TIFF2026518674000323.tif7170, bond length TIFF2026518674000324.tif7170 and bond angles The evaluation was based on TIFF2026518674000325.tif7170. Table 4 below shows the results for samples generated by Molecular Design Computation Model 115 (MDCM) trained on the QM9 molecular dataset, along with the mean and standard deviation over three runs. Figure 9A shows some examples of voxelized representations of molecules generated by Molecular Design Computation Model 115 trained on the QM9 molecular dataset and the corresponding molecular graphs. The cumulative distribution function (CDF) of strain energy for molecules generated by Molecular Design Computation Model 115 trained on the QM9 molecular dataset, compared to molecules in the QM9 molecular dataset and those generated by the conventional generative model EDM, is shown in Graph 1000 shown in Figure 10A. Figure 10B shows Graph 1050, which shows the empirical distribution of the number of atoms per molecule in the QM9 molecular dataset, compared to the empirical distribution of the number of atoms in molecules generated by Molecular Design Computation Model 115 trained on the QM9 molecular dataset.

[0198] [Table 4]

[0199] In some cases, the molecular design computation model 115 is also trained on a molecular geometric ensemble (GEOM) drug dataset before being applied to generate 10,000 samples. A comparison of these samples with the 10,000 samples generated by the conventional generative model EDM is shown in Table 5 below, along with the mean and standard deviation over three separate runs. Figure 9B shows several examples of voxelized representations of molecules generated by the molecular design computation model 115 (MDCM) trained on the molecular geometric ensemble (GEOM) drug dataset and the corresponding molecular graphs. The cumulative distribution function (CDF) of strain energy of molecules generated by the molecular design computation model 115 (MDCM) trained on the molecular geometric ensemble (GEOM) drug dataset, compared to molecules generated by the GEOM drug dataset and the conventional generative model EDM, is shown in Graph 1100, shown in Figure 11A. Figure 11B shows Graph 1150, which illustrates the empirical distribution of the number of atoms per molecule in the Geometric Ensemble of Molecules (GEOM) drug dataset, compared to the empirical distribution of the number of atoms in a molecule generated by Molecular Design Calculation Model 115 (MDCM) trained on the GEOM drug dataset.

[0200] [Table 5]

[0201] When the molecular design computation model 115 (MDCM) was trained on the QM9 dataset, it demonstrated comparable generative performance to the conventional generative model EDM. However, when the molecular design computation model 115 (MDCM) was trained on the Geometric Ensemble of Molecules (GEOM) drug dataset, a more challenging and realistic drug-like dataset than the QM9 dataset, it outperformed EDM by a considerably larger margin in eight of the nine metrics. For example, molecules generated by the molecular design computation model 115 (MDCM) trained on the GEOM drug dataset showed significantly lower median strain energy than those generated by EDM. Results from Tables 3 and 4 also show that augmenting the training dataset with rotation and translation improves the generative performance of the molecular design computation model 115 (e.g., MDCM no rot vs. MDCM). Overall, the molecular design computation model 115 is a more expressive model that scales better with the data. In particular, molecular design calculation model 115 is better able to capture many modes present in large-scale data distributions such as molecular geometric ensemble (GEOM) drug datasets.

[0202] Figure 12A is a schematic diagram showing a comparison of seed generation on a Geometric Ensemble of Molecules (GEOM) drug in different sampling iterations in discrete voxelization space and latent voxelization space, according to several exemplary embodiments. Panel 1210 shows molecular graphs of molecules generated in steps (or sampling iterations) 10, 20, 50, 100, and 200 by a molecular design computation model 115 that operates in latent voxelization space and updates the embedding of voxelized representations of seed molecules from a Geometric Ensemble of Molecules (GEOM) drug dataset. The corresponding voxelized representations of these molecules are shown in panel 1220. Panel 1215 shows molecular graphs of molecules generated in steps (or sampling iterations) 5, 10, 50, 100, and 200 by a molecular design computation model 115 that operates in discrete voxelization space and updates the voxelized representations of seed molecules from a Geometric Ensemble of Molecules (GEOM) drug dataset. The corresponding voxelized representations of these molecules are shown in panel 1225. As shown in Figures 12A and 12B, the molecular design computation model 115 can generate stable and effective intrinsic molecules that closely resemble seed molecules from the Geometric Ensemble of Molecules (GEOM) drug dataset, regardless of whether it operates in a latent voxelization space or a discrete voxelization space.

[0203] Table 6 below further shows the seed generation results (averaged over 5 iterations) for the geometric ensemble of molecules (GEOM) drug dataset.

[0204] [Table 6] TIFF2026518674000329.tif72170

[0205] Figure 12B is a schematic diagram showing a comparison of seed generation on PubChem drugs in different sampling iterations in discrete voxelization space and latent voxelization space according to several exemplary embodiments. Panel 1450 shows molecular graphs of molecules generated in steps (or sampling iterations) 10, 20, 50, 100, and 200 by molecular design computation model 115, which operates in latent voxelization space and updates the embedding of voxelized representations of seed molecules from the PubChem dataset. The corresponding voxelized representations of these molecules are shown in panel 1260. Panel 1255 shows molecular graphs of molecules generated in steps (or sampling iterations) 5, 10, 50, 100, and 200 by molecular design computation model 115, which operates in discrete voxelization space and updates the voxelized representations of seed molecules from the PubChem dataset. The corresponding voxelized representations of these molecules are shown in panel 1265. As shown in Figure 12B, the molecular design computation model 115 can also generate stable and effective intrinsic molecules that closely resemble seed molecules from the PubChem dataset, regardless of whether it is operating in a latent voxelization space or a discrete voxelization space.

[0206] Table 7 below further shows the seed generation results (averaged over 5 iterations) for the PubChem dataset.

[0207] [Table 7] TIFF2026518674000331.tif36170

[0208] Figure 12C shows molecular graphs of additional examples of molecules generated in steps (or sampling iterations) 10, 20, 50, 100, and 200 by molecular design computation model 115, which operates in a potential voxelization space and updates the embeddings of voxelized representations of two actual drug seed molecules. Figure 12D shows molecular graphs of several exemplary molecules generated in random selections (or sampling iterations) of steps by molecular design computation model, which operates in a potential voxelization space and updates the embeddings of random molecules (e.g., molecules with randomly selected atomic types and / or positions).

[0209] Table 8 below shows the seed generation results (averaged over 5 iterations) for five actual drugs.

[0210] [Table 8]

[0211] Figure 13 shows Graph 1300, which compares over time the number of stable, valid, and unique molecules generated by molecular design computation model 115 operating in a latent voxelization space, molecular design computation model 115 operating in a discrete voxelization space, and a state-of-the-art generative model. As shown in Figure 13, molecular design computation model 115 can generate far more stable, valid, and unique molecules than the state-of-the-art generative model, regardless of whether it is operating in a latent voxelization space or a discrete voxelization space. Furthermore, molecular design computation model 115 can generate more stable, valid, and unique molecules when operating in a latent voxelization space than when operating in a discrete voxelization space.

[0212] Table 9 below shows the potential voxelization space (MDCM). discrete ) Molecular design calculation model 115 that performs de novo generation in discrete voxelized space (MDCM latentThis paper compares the generative performance (averaged over the generative generation of 10,000 molecules in three iterations) of molecular design computation model 115, which performs de novo generative generation, and the state-of-the-art generative model EDM, for molecular geometric ensemble (GEOM) drugs.

[0213] [Table 9] TIFF2026518674000334.tif45170

[0214] Table 10 below shows a comparison of the production performance (averaged over the production of 10,000 molecules in three iterations) of molecular design computation models 115 performing de novo production in a latent voxelization space (MDCMlatent), molecular design computation model 115 performing de novo production in a discrete voxelization space (MDCMdiscrete), and state-of-the-art production models GSchNet and EDM for QM9 drugs.

[0215] [Table 10] TIFF2026518674000336.tif46170

[0216] Figure 14 depicts a block diagram showing an example of a computing system 1400 according to several exemplary embodiments. Referring to Figures 1 to 14, the computing system 1400 may be used to implement a molecular design engine 110, a training engine 120, a client device 130, and / or any component thereof.

[0217] As shown in Figure 14, the computing system 1400 may include a processor 1410, memory 1420, storage device 1430, and input / output device 1440. The processor 1410, memory 1420, storage device 1430, and input / output device 1440 may be interconnected via a system bus 1450. The processor 1410 is capable of processing instructions for execution within the computing system 1400. Such executed instructions may implement one or more components, such as a molecular design engine 110, an analysis engine 120, or a client device 130. In some exemplary embodiments, the processor 1410 may be a single-threaded processor. Alternatively, the processor 1410 may be a multi-threaded processor. The processor 1410 is capable of processing instructions stored in memory 1420 and / or storage device 1430 to display graphical information for a user interface provided via the input / output device 1440.

[0218] Memory 1420 is a computer-readable medium, such as volatile or non-volatile, that stores information within the computing system 1400. Memory 1420 can store, for example, data structures representing a configuration object database. Storage device 1430 is capable of providing persistent storage for the computing system 1400. Storage device 1430 may be a floppy disk device, a hard disk device, an optical disk device, or a tape device, or other suitable persistent storage means. Input / output device 1440 provides input / output operations for the computing system 1400. In some exemplary embodiments, input / output device 1440 includes a keyboard and / or a pointing device. In various implementations, input / output device 1440 includes a display unit for displaying a graphical user interface.

[0219] According to several exemplary embodiments, the input / output device 1440 may provide input / output operation for network devices. For example, the input / output device 1440 may include an Ethernet port or other networking port for communicating with one or more wired and / or wireless networks (e.g., a local area network (LAN), a wide area network (WAN), the Internet).

[0220] In some exemplary embodiments, the computing system 1400 may be used to run various interactive computer software applications that can be used for organizing, analyzing, and / or storing various forms of data. Alternatively, the computing system 1400 may be used to run any type of software application. These applications may be used to perform various functions, such as planning functions (e.g., generating, managing, and editing spreadsheet documents, word processing documents, and / or any other objects), computing functions, communication functions, etc. The application may include various add-in functions or may be a standalone computing product and / or function. When activated within an application, functionality may be used to generate a user interface provided via the input / output device 1440. The user interface may be generated by the computing system 1400 and presented to the user (e.g., on a computer screen monitor).

[0221] One or more aspects or features of the subject matter described herein may be realized in digital electronic circuits, integrated circuits, specially designed ASICs, field-programmable gate array (FPGA) computer hardware, firmware, software, and / or combinations thereof. These various aspects or features may include implementations in one or more computer programs executable and / or interpretable on a programmable system which includes at least one programmable processor, which may be special or general-purpose, coupled to receive data and instructions from a storage system, at least one input device, and at least one output device, and to transmit data and instructions to the storage system, at least one input device, and at least one output device. The programmable system or computing system may include clients and servers. Clients and servers are generally remote from each other and generally interact over a communication network. The relationship between clients and servers is created by computer programs running on each computer and having a client-server relationship with each other.

[0222] These computer programs, also called programs, software, software applications, applications, components, or code, contain machine instructions for a programmable processor and may be implemented in high-level procedural and / or object-oriented programming languages ​​and / or assembly / machine languages. As used herein, the term “machine-readable medium” means any computer program product, apparatus, and / or device used to provide machine instructions and / or data to a programmable processor, such as magnetic disks, optical disks, memory, and programmable logic devices (PLDs), and includes machine-readable medium that receives machine instructions as machine-readable signals. The term “machine-readable signals” means any signals used to provide machine instructions and / or data to a programmable processor. Machine-readable medium can store such machine instructions non-temporarily, such as non-temporarily solid-state memory, magnetic hard drives, or any equivalent storage medium. Machine-readable medium can, alternatively or additionally, store such machine instructions temporarily, such as processor caches or other random-access memories associated with one or more physical processor cores.

[0223] To provide user interaction, one or more aspects or features of the subject matter described herein may be implemented on a computer having, for example, a display device such as a cathode ray tube (CRT), liquid crystal display (LCD), or light-emitting diode (LED) monitor for displaying information to the user, and a keyboard and a pointing device such as a mouse or trackball, to which the user can provide input to the computer. User interaction may also be provided using other types of devices. For example, the feedback provided to the user may be any form of sensory feedback, such as visual feedback, auditory feedback, or tactile feedback, and input from the user may be received in any form, including acoustic, speech, or tactile input. Other possible input devices include touchscreens, or single-point or multi-point resistive or capacitive trackpads, speech recognition hardware and software, optical scanners, optical pointers, digital image capture devices, and other touch-sensitive devices such as associated interpretation software.

[0224] In the above description and claims, phrases such as "at least one of..." or "one or more of..." may appear, followed by a conjunctive list of elements or features. The term "and / or" may also be used in the enumeration of two or more elements or features. Unless implicitly or explicitly contradicted by the context in which it is used, such phrases are intended to mean either any of the enumerated elements or features individually, or any of the enumerated elements or features in combination with any of the other enumerated elements or features. For example, the phrases "at least one of A and B," "one or more of A and B," and "A and / or B" are intended to mean "A only, B only, or A and B together," respectively. The same interpretation is intended for lists containing three or more items. For example, the phrases "at least one of A, B, and C," "one or more of A, B, and C," and "A, B, and / or C" are intended to mean "A alone, B alone, C alone, A and B, A and C, B and C, or A, B, and C," respectively. The use of the term "based on" in the foregoing and in the claims is intended to mean "at least partially based" so that features or elements not enumerated are also permitted.

[0225] The subject matter described herein may be implemented in systems, apparatus, methods, and / or articles, depending on the desired configuration. The implementations described above do not necessarily represent all implementations of the subject matter described herein. Rather, they are merely some examples that correspond to the embodiments associated with the described subject matter. While several variations have been described in detail above, other modifications or additions are possible. In particular, further features and / or variations may be provided in addition to those described herein. For example, the aforementioned implementations may cover various combinations and partial combinations of the disclosed features, and / or combinations and partial combinations of some of the further features described herein. Furthermore, the logical flows shown in the accompanying drawings and / or described herein do not necessarily require a specific order or sequence shown to achieve the desired result. Other implementations may fall within the scope of the following claims.

Claims

1. A computer implementation method for identifying molecules having one or more desired properties, To generate a voxelized representation of the input molecule, Applying a molecular design calculation model to update the voxelized representation of the input molecule, The molecular design calculation model is trained to approximate the data distribution of one or more molecules exhibiting one or more desired properties by taking corrupted voxelized representations of one or more sample molecules exhibiting one or more desired properties as input and recovering the voxelized representations of the sample molecules from the corrupted voxelized representations. The molecular design calculation model updates and applies the voxelized representation of the input molecule in order to increase the likelihood that the resulting updated voxelized representation falls within the data distribution. At least based on the updated voxelized representation, a voxelized representation of the output molecule is generated, Computer implementation methods, including those mentioned above.

2. The method according to claim 1, wherein the voxelized representation of a molecule comprises a plurality of voxels organized into a three-dimensional voxel grid, and each atom in the molecule is represented as a continuous density across one or more voxels in the three-dimensional voxel grid.

3. The method according to claim 2, wherein the continuous density of each atom in the molecule is concentrated at the center of each atom, and a first voxel far from any atom in the molecule is associated with a lower atomic density value than a second voxel close to the center of an atom in the molecule.

4. The method according to claim 2 or 3, wherein each voxel in the three-dimensional voxel grid is associated with a value indicating the atomic density at a corresponding location.

5. The method according to any one of claims 1 to 4, wherein the voxelized representation of the molecule comprises one or more channels, each channel corresponding to a type of atom present in the corresponding molecule.

6. The method according to any one of claims 1 to 5, wherein the voxelized representation of the input molecule represents both the type and position of one or more atoms present in the corresponding molecule.

7. The method according to any one of claims 1 to 6, wherein applying the molecular design calculation model to update the voxelized representation of the input molecule includes updating the voxelized representation of the input molecule on at least a function that outputs a value indicating the likelihood that the resulting updated voxelized representation falls within the data distribution.

8. The method according to claim 7, further comprising parameterizing the function using a plurality of parameters of the molecular design calculation model.

9. The method according to claim 7 or 8, wherein the function includes a score function, and the value output by the function includes a score indicating a local change in the density of the data distribution at the location of the updated voxelized representation.

10. The molecular design calculation model described above includes at least, A first updated voxelized representation is generated by updating the voxelized representation of the input molecule. A second updated voxelized representation is generated by updating the voxelized representation of the input molecule. Applying a function parameterized by the molecular design calculation model to determine a first value that represents a first local change in the density of the data distribution at a first location occupied by the first updated voxelized representation, Applying the function to determine a second value that represents a second local change in the density of the data distribution at a second location occupied by the second updated voxelized representation, and If the first and second values ​​indicate that the density of the data distribution is higher at the first location than at the second location, further update the first updated voxelized representation instead of the second updated voxelized representation. The method according to any one of claims 1 to 9, wherein the voxelized representation of the input molecule is updated by the method.

11. The method according to claim 10, wherein the molecular design calculation model is applied to further update the first updated voxelized representation until one or more criteria are met.

12. The method according to claim 11, wherein the one or more criteria include at least one of (i) that iterations of an update threshold amount for the voxelized representation of the input molecule have been performed, (ii) that the first value of the first updated voxelized representation satisfies one or more thresholds, and (iii) that an output molecule of the threshold amount has been generated.

13. The method according to any one of claims 10 to 12, wherein the molecular design calculation model is applied to further modify the first updated voxelized representation in place of the second updated voxelized representation, at least on the basis that the first and second values ​​indicate that the first updated voxelized representation is more likely to be within the data distribution than the second updated voxelized representation.

14. The method according to any one of claims 10 to 13, wherein the molecular design calculation model is applied to further modify the first updated voxelized representation in place of the second updated voxelized representation, at least on the basis that the first and second values ​​indicate that the first updated voxelized representation is sampled from a data distribution density region that is higher than that of the second updated voxelized representation.

15. The method according to any one of claims 1 to 14, wherein the data distribution is a noisy data distribution occupied by noisy voxelized representations of the molecules exhibiting the one or more desired characteristics, and the voxelized representation of the output molecule is generated by denoising the first updated voxelized representation in order to map the first updated voxelized representation from the noisy data distribution to the true data distribution of the molecules exhibiting the one or more desired characteristics.

16. The method according to any one of claims 1 to 15, further comprising converting the voxelized representation of the output molecule into a different representation of the output molecule.

17. The method according to claim 16, wherein the different representations of the output molecule include a one-dimensional representation and / or a two-dimensional representation of the output molecule.

18. The voxelized representation of the output molecule is at least, The position of one or more atoms in the output molecule is determined by detecting at least one peak in the multiple atomic density values ​​included in the voxelized representation of the output molecule, and Determining one or more interconnection bonds based on the positions of at least one or more atoms. The method according to claim 16 or 17, which is converted by...

19. At least one data processor, A memory for storing instructions that, when executed by the at least one data processor, result in an operation including the method according to any one of claims 1 to 18, A system equipped with these features.

20. A non-temporary computer-readable medium for storing instructions that, when executed by at least one data processor, result in an operation including the method according to any one of claims 1 to 18.

21. Identifying one or more sample molecules exhibiting desired properties, To generate a noisy voxelized representation of the aforementioned sample molecule, Adding noise to the noisy voxelized representation of the sample molecule to generate a corrupted voxelized representation of the sample molecule, Training a molecular design calculation model to approximate the data distribution of one or more molecules exhibiting the aforementioned desired characteristics, The training includes applying the molecular design calculation model to recover a noisy voxelated representation of the sample molecule from a corrupted voxelated representation of the sample molecule, Optionally, the voxelized representation of the output molecule is generated by applying at least the molecular design calculation model to denoise the voxelized representation of the input molecule, Computer implementation methods including

22. The method according to claim 21, wherein the noisy voxelized representation of the sample molecule comprises a plurality of voxels organized into a three-dimensional voxel grid, and each atom in the sample molecule is represented as a continuous density across one or more voxels in the three-dimensional voxel grid.

23. The method according to claim 22, wherein the continuous density of each atom in the sample molecule is concentrated at the center of each atom.

24. The method according to claim 22 or 23, wherein each voxel in the three-dimensional voxel grid is associated with a value indicating the atomic density at a corresponding location.

25. The method according to any one of claims 22 to 24, wherein a first voxel located away from any atom in the sample molecule is associated with a lower atomic density value than a second voxel located closer to the center of an atom in the sample molecule.

26. The method according to any one of claims 21 to 25, wherein the noisy voxelized representation of the sample molecule includes one or more channels, each channel corresponding to a type of atom present in the sample molecule.

27. The method according to any one of claims 21 to 26, wherein the noisy voxelized representation of the sample molecule represents both the type and position of one or more atoms present in the sample molecule.

28. The method according to any one of claims 21 to 27, wherein training the molecular design calculation model includes adjusting several parameters of the molecular design calculation model to reduce the difference between the recovered voxelized representation of the sample molecule generated by the molecular design calculation model and the noisy voxelized representation of the sample molecule.

29. The method according to claim 28, wherein the plurality of parameters of the molecular design calculation model parameterize a function, and the values ​​of the plurality of parameters are adjusted to output values ​​that indicate local changes in the density of the data distribution of molecules in which the function exhibits one or more desired properties.

30. The method according to any one of claims 21 to 29, wherein the molecular design calculation model denoises the voxelized representation of the input molecule by updating at least the atomic density of one or more voxels in at least one channel of the voxelized representation of the input molecule.

31. The method according to claim 30, wherein updating the atomic density of one or more voxels in the at least one channel of the voxelized representation of the input molecule corresponds to updating at least one of the types and / or locations of one or more atoms present in the input molecule.

32. The method according to any one of claims 1 to 31, wherein the molecular design calculation model denoises the voxelized representation of the input molecule over multiple iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling until one or more criteria are met.

33. The method according to claim 32, wherein the one or more criteria include at least one of (i) that a threshold amount iteration of gradient-based Markov chain Monte Carlo (MCMC) sampling has been performed; (ii) that the voxelized representation of the output molecule has been sampled from a region having a threshold density; and (iii) that a threshold amount of output molecule has been generated.

34. The molecular design calculation model described above includes at least, Applying a first update to the voxelized representation of the input molecule to generate a first updated voxelized representation, Applying a second update to the voxelized representation of the input molecule to generate a second updated voxelized representation, and When it is determined that the first updated voxelized representation is sampled from a higher density region of the data distribution than the second updated voxelized representation, the first updated voxelized representation is further updated. The method according to any one of claims 21 to 33, wherein a voxelized representation of the output molecule is generated by the method.

35. The method according to claim 34, wherein the data distribution is a noisy data distribution occupied by noisy voxelized representations of the molecules exhibiting the one or more desired characteristics, and the voxelized representation of the output molecules is further generated by denoising the first updated voxelized representation in order to map the first updated voxelized representation to the true data distribution of the molecules exhibiting the one or more desired characteristics from the noisy data distribution.

36. Converting the voxelized representation of the output molecule to a different representation of the output molecule, The method according to any one of claims 21 to 35, further comprising:

37. The method according to claim 36, wherein the different representations of the output molecule include a one-dimensional representation and / or a two-dimensional representation of the output molecule.

38. Training the aforementioned molecular design calculation model is Applying the molecular design calculation model having the first adjustment to denoise the damaged voxelated representation of the sample molecule and to generate a first recovered voxelated representation of the sample molecule, Determine a first mean squared error (MSE) that quantifies the first difference between the first recovered voxelized representation and the noisy voxelized representation of the sample molecule, Applying the molecular design calculation model having a second adjustment to denoise the damaged voxelated representation of the sample molecule and to generate a second recovered voxelated representation of the sample molecule, Determine a second mean squared error (MSE) that quantifies the second difference between the second recovered voxelized representation and the noisy voxelized representation of the sample molecule, When determining that the first mean squared error (MSE) is smaller than the second mean squared error (MSE), the molecular design calculation model having the first adjustment instead of the second adjustment is further adjusted. The method according to any one of claims 21 to 37, including the method described in any one of claims 21 to 37.

39. At least one data processor, A memory for storing instructions that, when executed by the at least one data processor, result in an operation including the method according to any one of claims 21 to 38, A system equipped with these features.

40. A non-temporary computer-readable medium for storing instructions that, when executed by at least one data processor, result in an operation including the method according to any one of claims 21 to 38.

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